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Old 2020-04-11, 18:53   #12
mart_r
 
mart_r's Avatar
 
Dec 2008
you know...around...

25·19 Posts
Default Called out in the dark

(I always cringe a little when I see my hastily written post # 8 above with "q=2p", where I meant to say that q equals twice a prime number; might as well have written "q: prime"...)

Well, here's the data as of 2020-04-09. q=934 was a close one in terms of CSG value.
Code:
q: common difference in arithmetic progression p+k*q
CSG: Cramér-Shanks-Granville ratio via gap/phi(q)/log(p')² where p'=p+gap
CSG_max: maximum value found for CSG up to p_limit
p: initial prime of the gap
p_limit: search limit for p'

   q  CSG_max          gap             p       p_limit
   2  0.7394648022     210      20831323    3600000000
   4  0.7678340865     684    1464395089    7200000000
   6  0.7541322181     462      39895309   10800000000
   8  0.7436946715    1424    3176384429   14400000000
  10  0.8043339165    1610    5189671259   18000000000
  12  0.8052809769    1740   12411153017   21600000000
  14  0.8096072055    2310    2955286913   25200000000
  16  0.9046153418    3728    7194688583   28800000000
  18  0.7887450235     702        194027   32400000000
  20  0.7944296249    1600       7775737   36000000000
  22  0.8617839921    2002       4160719   39600000000
  24  0.7948892517    3720   31920285041   43200000000
  26  0.7982175172    5694   38786373547   46800000000
  28  0.8452080697    3836     279251711   50400000000
  30  0.8058232068    1980      40846943   54000000000
  32  0.8965150715    3808      11911369   57600000000
  34  0.8182937153    3876      29673503   61200000000
  36  0.7872577337    5400   24166901071   64800000000
  38  0.8518980455    2280        195271   68400000000
  40  0.8172390325    6360    3785091139   72000000000
  42  0.8251402679    3780     305816297   75600000000
  44  0.7778447835    1980         77369   79200000000
  46  0.8034522392    7268     640376543   82800000000
  48  0.7973452005    7344   26302298977   86400000000
  50  0.8793539278    4950      19315399   90000000000
  52  0.7726636783    7332     432150907   93600000000
  54  0.7956494153    7344    6831679457   97200000000
  56  0.7926567144    5376      19980397  100800000000
  58  0.7831435896    8932     582284587  104400000000
  60  0.7533972457    6180    6814968631  108000000000
  62  0.7480209472   13392   40678798409  111600000000
  64  0.8613806693    7104       9370547  115200000000
  66  0.7637963086    9834  104493100477  118800000000
  68  0.7981407159   13056    6594265703  122400000000
  70  0.8282785007   11900   42252957959  126000000000
  72  0.8602785358    4824       4344187  129600000000
  74  0.9131005021    9620      26876579  133200000000
  76  0.8416067457   16796   16804480523  136800000000
  78  0.7510340136    9828   13836158729  140400000000
  80  0.7585177824   10720    1339392487  144000000000
  82  0.8163798773    2214          1553  147600000000
  84  0.8017445129   11172   29153099231  151200000000
  86  0.8236614027    9718      19002559  154800000000
  88  0.8074176319    3344         22907  158400000000
  90  0.7952351245    8460    1391789947  162000000000
  92  0.8569074437   19320    6775293947  165600000000
  94  0.7540215308   21244   55988532973  169200000000
  96  0.7835562193    6816      14461861  172800000000
  98  0.8195247347   12936     262621343  176400000000
 100  0.7274868378   15500   10549382033  180000000000
 102  0.7887967496   16626  139972076507  183600000000
 104  0.7885883689   24648  120860909123  187200000000
 106  0.7406871356   15900     666737879  190800000000
 108  0.8456207760   20196  153489937273  194400000000
 110  0.7577236448    8250      14618897  198000000000
 112  0.8754122474   19376    2117717087  201600000000
 114  0.7615636029    9348     104547589  205200000000
 116  0.7729502356   26796   63916863757  208800000000
 118  0.8167041620   20886    1316371417  212400000000
 120  0.8057216311   14040   13628678729  216000000000
 122  0.7947909820   28182   36113593211  219600000000
 124  0.8316652784   30628   57483096991  223200000000
 126  0.9142860299   18270   17061510127  226800000000
 128  0.8323761564    7296        113623  230400000000
 130  0.7938556043   21450   20138027813  234000000000
 132  0.7846464407   10560      92494289  237600000000
 134  0.8397671201   14740      12075073  241200000000
 136  0.7672983613   26928   14785702759  244800000000
 138  0.7924769327   15042    1047660137  248400000000
 140  0.7831617970    8400       3096061  252000000000
 142  0.8088733993   12780       3334549  255600000000
 144  0.7893617069   17856    2678906773  259200000000
 146  0.8196507109   23652     494696261  262800000000
 148  0.7782739647   38480  240275550413  266400000000
 150  0.7468321094    6300       2020723  270000000000
 152  0.7468621394   28120    8536597477  273600000000
 154  0.9369830338   35728   88779374809  277200000000
 156  0.7985008265   13728     165640219  280800000000
 158  0.7393182535   39816  258043969397  284400000000
 160  0.7853708350   28960   26578052863  288000000000
 162  0.8258805846   26244   34294519837  291600000000
 164  0.7735979649   35260   23242155967  295200000000
 166  0.8175587888   42828   94831438649  298800000000
 168  0.7739486136   24864  171996125029  302400000000
 170  0.7905258192   29240   27579604799  306000000000
 172  0.8745407940   38356    8387732083  309600000000
 174  0.8966388328   14616      25666717  313200000000
 176  0.8893387228   32912    2191630061  316800000000
 178  0.7718247316   44856  144798233893  320400000000
 180  0.7968104593   22680   37641351263  324000000000
 182  0.8820202987   27482    1082590961  327600000000
 184  0.8446274883   41032   15996631921  331200000000
 186  0.8021152848   15624      66824477  334800000000
 188  0.7964246226   40044   14217429113  338400000000
 190  0.8735201597   38950   64231886011  342000000000
 192  0.8583746127   11904       2459623  345600000000
 194  0.8234255916   44232   18757576997  349200000000
 196  0.8703957715   44100   46355125469  352800000000
 198  0.7511941018   20196    1560142237  356400000000
 200  0.8255106246   39800   45870059471  360000000000
 202  0.8455991259   26462      48134069  363600000000
 204  0.8383878988   31212   29818321129  367200000000
 206  0.8849004882   20806       3903223  370800000000
 208  0.8637254761   47008   21908990083  374400000000
 210  0.7536441567   13230     202008439  378000000000
 212  0.8726800198   57028   76983450889  381600000000
 214  0.8300985533   54570   65376711233  385200000000
 216  0.8565309700   38016   60639375773  388800000000
 218  0.8000713650   60386  302626514693  392400000000
 220  0.8516677011   11220        363019  396000000000
 222  0.7476242389   35964  168120545239  399600000000
 224  0.7530876774   27552     300702751  403200000000
 226  0.8205657931   65314  378168298933  406800000000
 228  0.7687388396   35568  102156515693  410400000000
 230  0.8278708905   49910  232943726651  414000000000
 232  0.7860150605   25288      22918543  417600000000
 234  0.7932876948   27144    2934877793  421200000000
 236  0.8808741581   53100    7947586583  377600000000
 238  0.7961571214   47838   73308073691  380800000000
 240  0.7746515981   25440    6883929373  384000000000
 242  0.8312839360   32912     173468021  387200000000
 244  0.8153157728   64172  132595555181  390400000000
 246  0.8801251829   47478  189457586089  393600000000
 248  0.8449133277   22816       3249793  396800000000
 250  0.9603210373   53000   15946776179  400000000000
 252  0.8886298435   37800   35983220659  403200000000
 254  0.7778963787   45974    2545430123  406400000000
 256  0.7680769257   53248   12798115129  409600000000
 258  0.7684771240   45150  305996132599  412800000000
 260  0.7724350668   30160     573522601  416000000000
 262  0.7939284070   51352    4866855997  419200000000
 264  0.8241313527   46200  313621476739  422400000000
 266  0.8801702481   39368     688831433  425600000000
 268  0.7914716927   71020  210484888321  428800000000
 270  0.9385992389   27000     479487689  432000000000
 272  0.7985388488   59568   30497191399  435200000000
 274  0.9241529945   68500   13766905759  438400000000
 276  0.8452548271   33672    1738757609  441600000000
 278  0.8930499724   25854       1925299  444800000000
 280  0.7989596541   52360  222398285827  448000000000
 282  0.8508107698   23406      32332831  451200000000
 284  0.8785941526   66456   12436366727  454400000000
 286  0.7858974077   62920  165094766113  457600000000
 288  0.7935760257   50688  159328991309  460800000000
 290  0.7542062497   60610  429818619523  464000000000
 292  0.8835286349   35624      18463427  467200000000
 294  0.8874698444   31458     834434033  470400000000
 296  0.7407823594   59792   19144263221  473600000000
 298  0.8142218681   71520   38040537103  476800000000
 300  0.8694555188   31500    1746213839  480000000000
 302  0.7889783882   46206     381321631  483200000000
 304  0.9026153946   44688     112884059  486400000000
 306  0.8374812598   13464        403553  489600000000
 308  0.8043192128   57288   38073581723  492800000000
 310  0.8496494922   69750  228639573389  496000000000
 312  0.8318902760   51168   98393397133  499200000000
 314  0.8034115353   51810     676001831  502400000000
 316  0.7761217516   36024      30954479  505600000000
 318  0.8218376546   39114    1952210459  508800000000
 320  0.8298538635   68480  106433008811  512000000000
 322  0.8573533053   54740    3560039459  515200000000
 324  0.7994627901   61560  394806744763  518400000000
 326  0.8083900200   80848   61763668063  521600000000
 328  0.7963256514   70848   17418374759  524800000000
 330  0.7638121358   28380    2288156501  528000000000
 332  0.7948104095   73704   21234656767  531200000000
 334  0.7853352422   91850  337046857421  534400000000
 336  0.7538847566   48720  185386505651  537600000000
 338  0.8637454324   43602      64873867  540800000000
 340  0.8240596233   65280   63699574657  544000000000
 342  0.8010075672   59850  264946609777  547200000000
 344  0.9190160329   66736    1069426291  550400000000
 346  0.7997930054   84078   54543153053  553600000000
 348  0.8268505391   67512  532187265079  556800000000
 350  0.8106891221   61950   91077187501  560000000000
 352  0.7785409404   82720  155422575103  563200000000
 354  0.8053164792   59826   97833706423  566400000000
 356  0.8760991508  102172  151136306521  427200000000
 358  0.7782235660   36516      11215003  429600000000
 360  0.9190759335   23760      13367671  432000000000
 362  0.7574134126   91224  171412985833  434400000000
 364  0.7756310715   51324    2040279533  436800000000
 366  0.8000166747   25986      13943863  439200000000
 368  0.7748084867   91632  181059672907  441600000000
 370  0.7987557798   81400  357568042813  444000000000
 372  0.7688792740   42408    2045612389  446400000000
 374  0.8532053339   58344     951272459  448800000000
 376  0.8393024208   62040     506537617  451200000000
 378  0.7935133452   61236  406541144927  453600000000
 380  0.8062842535   70680   51924372169  456000000000
 382  0.7889373294   90916   49616984707  458400000000
 384  0.7939465677   43392     941956339  460800000000
 386  0.7891241447   86850   24998032091  463200000000
 388  0.8235266859   72556    2009863117  465600000000
 390  0.7826368919   45240   45380958619  468000000000
 392  0.8571708876   75656    9004407101  470400000000
 394  0.8099475511   32308       1536583  472800000000
 396  0.8578841605   68904  172082709217  475200000000
 398  0.8791459095   89152    6737268127  477600000000
 400  0.7989545605   12800          9371  480000000000
 402  0.7868411869   66732  101933130811  482400000000
 404  0.7941196209   83628    9237777071  484800000000
 406  0.8585658511   87696   51121166533  487200000000
 408  0.8204181763   66912   91749328751  489600000000
 410  0.7897091793   46740     225303313  492000000000
 412  0.8036159885   90228   15439142689  494400000000
 414  0.8961928199   80730  221437110397  496800000000
 416  0.8020117468   75296    4013157443  499200000000
 418  0.7948806774  102410  415898213609  501600000000
 420  0.7627980893   26880     209227433  504000000000
 422  0.8690265566   57814      53634703  506400000000
 424  0.7602757566   91584   28278509927  508800000000
 426  0.7914098117   71994  117628436659  511200000000
 428  0.8044283310   40660       5039641  513600000000
 430  0.8013985116   55470     653446711  516000000000
 432  0.8219377815   53568    1734713993  518400000000
 434  0.7549037817   59458    1215100363  520800000000
 436  0.8047788797  102896   36828863651  523200000000
 438  0.7961083251   57816    5663148871  525600000000
 440  0.8792757227   58520     720313157  528000000000
 442  0.7596162182   99450  219117304141  530400000000
 444  0.9438876646   15984         35257  532800000000
 446  0.7775995907   49060      20910913  535200000000
 448  0.7848311396   90944   46689332597  537600000000
 450  0.7619657101   57600   79481983369  540000000000
 452  0.7838385407   97632   17418654119  542400000000
 454  0.7682744177  118948  232873806283  544800000000
 456  0.8469687305   11856          7283  547200000000
 458  0.8209257626   71448     305532509  549600000000
 460  0.7705031462   72680   11329574903  552000000000
 462  0.8277181464   44814    1678178797  554400000000
 464  0.8354396498   55680      30933989  556800000000
 466  0.8675896733   26562         70937  559200000000
 468  0.7753222048   80496  458518937557  561600000000
 470  0.8680891345   94000   34320032563  564000000000
 472  0.8363640483   66080     103334411  566400000000
 474  0.8380885352   81528   69987740731  568800000000
 476  0.9122603335   97580   17812528859  571200000000
 478  0.8459786783   58316      24551903  573600000000
 480  0.8369451486   55200    7215375371  576000000000
 482  0.8084758201   85796    1355943101  578400000000
 484  0.7928372491   60984     131951387  580800000000
 486  0.9670602256   66582     897783067  583200000000
 488  0.8040919055  124928  112158744989  585600000000
 490  0.8378578846   82320   31813190909  588000000000
 492  0.7739373512   71340   26551217113  590400000000
 494  0.8392228848   79040    1171149593  592800000000
 496  0.7869001503   98704    8483101717  595200000000
 498  0.7903333451   86652  169488659107  597600000000
 500  0.7914911855  105000  153153439729  600000000000
 502  0.9346253968   41164        540139  602400000000
 504  0.8170280734   50400     974403323  604800000000
 506  0.8272732557   71852     425671457  607200000000
 508  0.8267616819  112776   12711671711  609600000000
 510  0.8611973391   44880     579426871  612000000000
 512  0.7850984980  121344   46897900787  614400000000
 514  0.7873373864   55512      16064987  616800000000
 516  0.8019834578   72756   12362133493  619200000000
 518  0.8366088676  101010   18527678629  621600000000
 520  0.8696185442  109200  127816392311  624000000000
 522  0.7983405988   46458     120978283  626400000000
 524  0.8097368830  154580  586125879281  628800000000
 526  0.8115530554   94680    1460084749  631200000000
 528  0.8934942692   34848       5998913  633600000000
 530  0.8049360188   57240     107123117  636000000000
 532  0.7920246624   30324        575077  532000000000
 534  0.8161638595   88110   57019930549  534000000000
 536  0.7799025504  138288  179982795691  536000000000
 538  0.9016955220  112980    2457304483  538000000000
 540  0.8029054239   48060     715228027  540000000000
 542  0.8534940538   61246      11964913  542000000000
 544  0.8392434214  126208   33574445479  544000000000
 546  0.8193290227   16380        114593  546000000000
 548  0.8034500145   96996    1410813787  548000000000
 550  0.7885921427  109450  275839875067  550000000000
 552  0.7650231302   60720    1669752961  552000000000
 554  0.7914668223  147364  190546085857  554000000000
 556  0.8516820096  150676   98958026977  556000000000
 558  0.9544916211  106020   61428637987  558000000000
 560  0.7749958441   75040    5660034091  560000000000
 562  0.7812147343  151740  274490495683  562000000000
 564  0.7860473296   62604    1085107883  564000000000
 566  0.7891020079  127916   25853082041  566000000000
 568  0.8409819101   71568      37194763  568000000000
 570  0.8015346996   27930       5671207  570000000000
 572  0.7872642046  100100    9913066937  572000000000
 574  0.8355665622  104468    8173667093  574000000000
 576  0.7897361686  103680  227188645297  576000000000
 578  0.7884091107  106352    4694158901  578000000000
 580  0.8716154868  135720  282082451569  580000000000
 582  0.7289731501   73332    8727166157  582000000000
 584  0.7923222032  106872    2504438459  584000000000
 586  0.8159773780  133608   19239163373  586000000000
 588  0.7761971881   58212    1499370799  588000000000
 590  0.8344010904  123900   97104120731  590000000000
 592  0.9093598272  152736   30757758641  592000000000
 594  0.8203596194  103950  333275730829  594000000000
 596  0.8752581666  116220    1578834337  596000000000
 598  0.7933508876  113022   12263164867  598000000000
 600  0.7956697951   19200        196303  600000000000
 602  0.8671990408   55986       8882693  602000000000
 604  0.8070806533  103284     932676103  604000000000
 606  0.7796492138   96960   67559839063  606000000000
 608  0.8125159769  141664   48492135667  608000000000
 610  0.8365143363   40260       1372451  610000000000
 612  0.7978540809   44064      23167169  612000000000
 614  0.8275383515   68768      14281613  614000000000
 616  0.7562342777  116424   99877977587  616000000000
 618  0.8265107359  111240  142939098451  618000000000
 620  0.7625254531   44640       6020933  620000000000
 622  0.8063729000   93300     245534483  622000000000
 624  0.9394014419  132288  577632351979  624000000000
 626  0.8003908014  170898  229723986623  626000000000
 628  0.8690691013  152604   20089808047  628000000000
 630  0.7795321897   76860  231276114073  630000000000
 632  0.8457792089  182648  266552475209  632000000000
 634  0.8321349317  178154  201487337099  634000000000
 636  0.8465112163   94128   11000930573  636000000000
 638  0.7538727012   93148    1327646743  638000000000
 640  0.9120077454   55040       4602251  640000000000
 642  0.8152602768   77040    1475945477  642000000000
 644  0.8303242949   97244    1403478863  644000000000
 646  0.9148101139  191862  524463691699  646000000000
 648  0.8487263784   57024      45602917  648000000000
 650  0.7783532479   57850      43857397  650000000000
 652  0.8380466032  132356    3876681503  391200000000
 654  0.9214740453   51666       9881863  392400000000
 656  0.7679775506   82000      85638121  393600000000
 658  0.8049383681  151998  228935733461  394800000000
 660  0.7563398502   27060       3093703  396000000000
 662  0.7767298220  179402  308765222369  397200000000
 664  0.8497732615  179944  108343097587  398400000000
 666  0.9612073070  137196  145879569457  399600000000
 668  0.8291122833  161656   33463509787  400800000000
 670  0.8588802430  146730  111632773561  402000000000
 672  0.8377544361   92064   24553355279  403200000000
 674  0.8927385746  154346    7102999643  404400000000
 676  0.7911246648   81120      74589533  405600000000
 678  0.8188167676  101700   16846380763  406800000000
 680  0.7847062189  129880  110374441477  408000000000
 682  0.8756801286  157542   43180032209  409200000000
 684  0.8371047755   63612     139850671  410400000000
 686  0.8425141547  118678    3207660733  411600000000
 688  0.7914089252   87376      74464177  412800000000
 690  0.8298009290   93150   92923597009  414000000000
 692  0.8099695701  189608  213400291319  415200000000
 694  0.9352046150  222080  238517976413  416400000000
 696  0.8663493208   64728      85359893  417600000000
 698  0.7797477822   45370        367369  418800000000
 700  0.8284455357  136500  239460526523  420000000000
 702  0.7511986045   32292       1306499  421200000000
 704  0.8202954082  187264  397943965597  422400000000
 706  0.8695438095   40242         55201  423600000000
 708  0.8977861205  144432  273087013487  424800000000
 710  0.7724598204  149810  269015016161  426000000000
 712  0.7796816198  153792   19083648461  427200000000
 714  0.7697989836   37842       8857367  428400000000
 716  0.7831859227  193320  272750735171  429600000000
 718  0.7661030339  186680  214029806201  430800000000
 720  0.8760847971  119520  377221918061  432000000000
 722  0.7617166259  131404    5674164913  433200000000
 724  0.7975329263  110772     339112381  434400000000
 726  0.8799338964  137940  391674855421  435600000000
 728  0.9518517909  184184  180789356273  436800000000
 730  0.8169767948   59130       7609781  438000000000
 732  0.8289374951   34404        479797  439200000000
 734  0.8603414239  198180   78573408271  440400000000
 736  0.7940567828   36064         49669  441600000000
 738  0.8187851952   69372     144447397  442800000000
 740  0.8024558855  102120    1346388959  444000000000
 742  0.8270690786   48972        912367  445200000000
 744  0.7697508611  124992  197934069341  446400000000
 746  0.8040409658  181278   49168511023  447600000000
 748  0.7830564314  139128   17115875771  448800000000
 750  0.8359892306  106500   91377216071  450000000000
 752  0.7749013078  128592    1668673339  451200000000
 754  0.7782240049  183222  313412732261  452400000000
 756  0.7984514297   71820     728533909  453600000000
 758  0.8307863368  161454    7035777923  454800000000
 760  0.8587348951  151240   54915038317  456000000000
 762  0.7947601914  132588  149362737379  457200000000
 764  0.8072228398  182596   39444378481  458400000000
 766  0.8360220240  124092     363645049  459600000000
 768  0.8159361794  104448    5146249133  460800000000
 770  0.8512445396   80850     435991117  462000000000
 772  0.7934001992  214616  336250303541  463200000000
 774  0.7963577306   77400     338022701  464400000000
 776  0.8694867562   95448      21931331  465600000000
 778  0.7896427008  161046    9056973697  466800000000
 780  0.7579427233   30420       1870951  468000000000
 782  0.7925574832  168912   48563547259  469200000000
 784  0.8187678710   40768        152791  470400000000
 786  0.7375163313  128904  182041921063  471600000000
 788  0.8598576323  115836     112344431  472800000000
 790  0.7449992657  116130    5097460699  474000000000
 792  0.7809066212  131472  318121728761  475200000000
 794  0.8737191630  146096     839726627  476400000000
 796  0.8171350137  216512  171358508429  477600000000
 798  0.8189774650  110124   68522931313  478800000000
 800  0.7854380237  124000    4429597201  480000000000
 802  0.8127895345  231778  394291297993  481200000000
 804  0.7850960183  134268  113158700561  482400000000
 806  0.9079408402   82212       7638601  483600000000
 808  0.7877421483  113120     169209149  484800000000
 810  0.8116850129   89910    6836640043  486000000000
 812  0.8851736046  157528    9883553821  487200000000
 814  0.7938088485  104192     196064567  488400000000
 816  0.8066643398   61200      29890303  489600000000
 818  0.8335856530  112884      81576293  490800000000
 820  0.8731640737   90200      63450923  492000000000
 822  0.8762643516  110970    2349421741  493200000000
 824  0.8675619063  149144     821531663  494400000000
 826  0.7608164263  191632  482975333977  495600000000
 828  0.7652805026   90252    1510362617  496800000000
 830  0.9773893526  154380    3391062847  498000000000
 832  0.8327364626  114816     169459867  499200000000
 834  0.8070598355   81732     208384291  500400000000
 836  0.7538505214  174724  104621735923  334400000000
 838  0.8485627499   66202        791251  335200000000
 840  0.8015664476   73920    3295891901  336000000000
 842  0.7876682549   71570       2370917  336800000000
 844  0.8376720882  181460    7295944001  337600000000
 846  0.8142049032   83754     242174417  338400000000
 848  0.8232748309  191648   18770276141  339200000000
 850  0.9701528945   68850       2865899  340000000000
 852  0.8246959945   74976      66856927  340800000000
 854  0.7816720250  118706     831340553  341600000000
 856  0.7892210034  221704  150881417317  342400000000
 858  0.7730683037   55770      33794983  343200000000
 860  0.7875830400  184040  283849393787  344000000000
 862  0.7629563985  160332    3988841561  344800000000
 864  0.8914155653   49248        986113  345600000000
 866  0.7871098852  122972     181431827  346400000000
 868  0.7913892342  123256    1079341177  347200000000
 870  0.8374583079   82650    1305824189  348000000000
 872  0.7561328839  190968   31683162491  348800000000
 874  0.7722875504  180044   34472439539  349600000000
 876  0.8255392548  135780   23908792657  350400000000
 878  0.8059992615  178234    5732050237  351200000000
 880  0.8181553201  134640    7058010781  352000000000
 882  0.8094486988   98784    3607715213  352800000000
 884  0.7567896075  177684   54800797889  353600000000
 886  0.8355161599  239220  113074220731  354400000000
 888  0.8258816962  101232     911045519  355200000000
 890  0.8369225223  100570     105642601  356000000000
 892  0.7741629232  202484   34734355067  356800000000
 894  0.8349591749   82248      83596313  357600000000
 896  0.8173757133  190848   51175902559  358400000000
 898  0.7948385029  204744   25932816499  359200000000
 900  0.8072861180  135000  290994718649  360000000000
 902  0.8232989477  217382  143887883981  360800000000
 904  0.7813795699  218768   71929518179  361600000000
 906  0.8341247493  126840    5993514403  362400000000
 908  0.8038721784  124396     108448177  363200000000
 910  0.8725257404   66430      11447977  364000000000
 912  0.7384255018  134064   80190699493  364800000000
 914  0.7934699183  232156  100197840751  365600000000
 916  0.8514071759  204268    9155647951  366400000000
 918  0.8050224606  136782   35374365181  367200000000
 920  0.8424586115   61640       1763849  368000000000
 922  0.7601528076  214826   58158071267  368800000000
 924  0.8530073203   69300      97746161  369600000000
 926  0.8116795701  221314   35526795583  370400000000
 928  0.8150834574  208800   24269915627  371200000000
 930  0.9064778846   68820      52930403  372000000000
 932  0.8943236869  212496    6725412643  372800000000
 934  0.9991973371  137298      28542649  373600000000 * largest CSG value so far
 936  0.8676912530   71136      21181103  374400000000
 938  0.8053687523  217616  221046403007  375200000000
 940  0.8089099343  177660   40714396309  376000000000
 942  0.8067961396   87606     126384917  376800000000
 944  0.8331691839  189744    4182919339  377600000000
 946  0.7755322031  197714   50103406523  378400000000
 948  0.7864516026  169692  263594116631  379200000000
 950  0.8545569452  122550     465470219  380000000000
 952  0.8405042747  119952     235628287  380800000000
 954  0.8998573515   60102       2200661  381600000000
 956  0.7626024207  247604  220062550277  382400000000
 958  0.8529434109  214592    9196163681  383200000000
 960  0.8904686989  120960   10093588667  384000000000
 962  0.8144970096   88504       7634353  384800000000
 964  0.8004216214  107004      17584639  385600000000
 966  0.8283176903  122682   19348856179  386400000000
 968  0.9204665049  279752  259460206361  387200000000
 970  0.8013154534  204670  158734118899  388000000000
 972  0.8225551898  150660   21178988759  388800000000
 974  0.7782865462  219150   28420213067  389600000000
 976  0.9105943329  278160   90346489859  390400000000
 978  0.7903996503  165282  107942471909  391200000000
 980  0.7846347168  117600    1487302123  392000000000
 982  0.8063698833  262194  153969081667  392800000000
 984  0.7799444190  169248  203888107831  393600000000
 986  0.7924196264  225794   89694739373  394400000000
 988  0.8062837244  204516   33384442471  395200000000
 990  0.7913342257   97020    6544493717  396000000000
 992  0.8327256129  248000   65733837647  396800000000
 994  0.8168423482  217686   87037919861  397600000000
 996  0.8046526420   66732       7982237  398400000000
 998  0.8287134801  212574    7185918043  399200000000
1000  0.8366128339  192000   25270575311  400000000000
Attached is all data for q <= 1000 as well as the VBA code I use.

I gave my workplace PC a well deserved rest over Easter. Calculations will continue on Wednesday.
Attached Files
File Type: zip results_all 2020-04-09.zip (613.7 KB, 89 views)
File Type: txt PGAP code.txt (4.1 KB, 84 views)
mart_r is offline   Reply With Quote
Old 2020-04-12, 20:23   #13
mart_r
 
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Dec 2008
you know...around...

25·19 Posts
Default


I notice that my code is well received, so I had to rewrite it a little and remove a bug that could give incorrect results (if any) when the starting point ps was less than d&. Attached is the new VBA code.
Attached Files
File Type: txt PGAP code.txt (4.4 KB, 99 views)
mart_r is offline   Reply With Quote
Old 2020-04-30, 15:07   #14
mart_r
 
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Dec 2008
you know...around...

25·19 Posts
Talking Let's go Turbo!

(Are any fans of Beyblade around here?)

While moving in the 12-digit range, I noticed how inefficient my program is. I sieve the same numbers over and over again for every q. Quick-and-dirty analysis: each q sieves about 0.81 times (i.e. 8/pi²) the amount of numbers as the "base" interval (at q=2) while practically searching the same range for p. The thought of re-writing my program did hang around in my head for some time, but only recently I found out how urgent it is, and it took a whole weekend to come up with a satisfying solution that worked properly.

All q <= 1000 are now searched up to p=8*1011, progressing at a speed of about 4.8*109 per hour, and another instance running in parallel searches 1000 < q <= 2690, currently at p=7.3*1010, and a throughput of about 2.3*109 per hour. I also have a plan in mind to take all q <= 30030 up to at least 1010, but I have yet to test if it works.

Code:
q: common difference in arithmetic progression p+k*q
CSG: Cramér-Shanks-Granville ratio via gap/phi(q)/log(p+gap)²
CSG_max: maximum value found for CSG up to p=8*10^11
p: prime preceding the gap

current record for CSG_max: 0.9991973371 @ q=934

   q  CSG_max          gap             p
   2  0.7953486740     456   25056082087     
   4  0.8056652398    1044  113391385573     
   6  0.7541322181     462      39895309     
   8  0.7875867918    2080  144309631099     
  10  0.8930327253    2450  236455710509     
  12  0.8455173596    2352  283661812859     
  14  0.8345982115    2884   26448217657     
  16  0.9046153418    3728    7194688583     
  18  0.7887450235     702        194027     
  20  0.7944296249    1600       7775737     
  22  0.8617839921    2002       4160719     
  24  0.8117145259    4392  197036728351     
  26  0.8652413900    7540  505084610521     
  28  0.8452080697    3836     279251711     
  30  0.8058232068    1980      40846943     
  32  0.8965150715    3808      11911369     
  34  0.8182937153    3876      29673503     
  36  0.7872577337    5400   24166901071     
  38  0.8518980455    2280        195271     
  40  0.8172390325    6360    3785091139     
  42  0.8251402679    3780     305816297     
  44  0.8085714112   11132  248049290057     
  46  0.8034522392    7268     640376543     
  48  0.7973452005    7344   26302298977     
  50  0.8793539278    4950      19315399     
  52  0.7811165997   13832  626287370141     
  54  0.7956494153    7344    6831679457     
  56  0.8531838024   13272  113946560627     
  58  0.8160213701   17052  731647597039     
  60  0.7594431944    8760  457941678127     
  62  0.7505368847   16740  694602632629     
  64  0.8613806693    7104       9370547     
  66  0.7637963086    9834  104493100477     
  68  0.7981407159   13056    6594265703     
  70  0.8282785007   11900   42252957959     
  72  0.8602785358    4824       4344187     
  74  0.9131005021    9620      26876579     
  76  0.8416067457   16796   16804480523     
  78  0.7510340136    9828   13836158729     
  80  0.8244076217   19680  727457191561     
  82  0.8163798773    2214          1553     
  84  0.8017445129   11172   29153099231     
  86  0.8236614027    9718      19002559     
  88  0.8173745127   22528  251192223571     
  90  0.7952351245    8460    1391789947     
  92  0.8569074437   19320    6775293947     
  94  0.7540215308   21244   55988532973     
  96  0.7963941131   17280  203618303897     
  98  0.8195247347   12936     262621343     
 100  0.7442402852   20600  265671964073     
 102  0.7887967496   16626  139972076507     
 104  0.9499776231   31200  229169128997     
 106  0.9015411061   33072  342820240309     
 108  0.8456207760   20196  153489937273     
 110  0.7957899312   21780  229165433009     
 112  0.8754122474   19376    2117717087     
 114  0.8493019884   22116  478998886567     
 116  0.7977964383   32248  465563693299     
 118  0.8167041620   20886    1316371417     
 120  0.8057216311   14040   13628678729     
 122  0.7947909820   28182   36113593211     
 124  0.8316652784   30628   57483096991     
 126  0.9142860299   18270   17061510127     
 128  0.8323761564    7296        113623     
 130  0.7938556043   21450   20138027813     
 132  0.7846464407   10560      92494289     
 134  0.8397671201   14740      12075073     
 136  0.7672983613   26928   14785702759     
 138  0.7924769327   15042    1047660137     
 140  0.9112585981   31360  425297500759     
 142  0.8610872285   43026  401037154541     
 144  0.7893617069   17856    2678906773     
 146  0.8196507109   23652     494696261     
 148  0.7830010017   42328  794519516383     
 150  0.7557605255   21000  279561600257     
 152  0.7675315249   38456  286089015071     
 154  0.9369830338   35728   88779374809     
 156  0.7985008265   13728     165640219     
 158  0.7606501324   43134  512782039607     
 160  0.8211887580   36960  328840371359     
 162  0.8258805846   26244   34294519837     
 164  0.7924402630   47232  714913847737     
 166  0.8175587888   42828   94831438649     
 168  0.7739486136   24864  171996125029     
 170  0.7905258192   29240   27579604799     
 172  0.8745407940   38356    8387732083     
 174  0.8966388328   14616      25666717     
 176  0.8893387228   32912    2191630061     
 178  0.7718247316   44856  144798233893     
 180  0.7968104593   22680   37641351263     
 182  0.8820202987   27482    1082590961     
 184  0.8892744577   56856  508307558683     
 186  0.8021152848   15624      66824477     
 188  0.7964246226   40044   14217429113     
 190  0.8735201597   38950   64231886011     
 192  0.8583746127   11904       2459623     
 194  0.8234255916   44232   18757576997     
 196  0.8703957715   44100   46355125469     
 198  0.7511941018   20196    1560142237     
 200  0.8255106246   39800   45870059471     
 202  0.8455991259   26462      48134069     
 204  0.8383878988   31212   29818321129     
 206  0.8849004882   20806       3903223     
 208  0.8637254761   47008   21908990083     
 210  0.7941670680   27510  464338653979     
 212  0.8726800198   57028   76983450889     
 214  0.8300985533   54570   65376711233     
 216  0.8565309700   38016   60639375773     
 218  0.8025184444   64746  741341656273     
 220  0.8516677011   11220        363019     
 222  0.7476242389   35964  168120545239     
 224  0.7530876774   27552     300702751     
 226  0.8205657931   65314  378168298933     
 228  0.7687388396   35568  102156515693     
 230  0.8278708905   49910  232943726651     
 232  0.7860150605   25288      22918543     
 234  0.7932876948   27144    2934877793     
 236  0.9437796854   79296  487692833143     
 238  0.7961571214   47838   73308073691     
 240  0.8040958748   37680  564376543243     
 242  0.8312839360   32912     173468021     
 244  0.8153157728   64172  132595555181     
 246  0.8801251829   47478  189457586089     
 248  0.8449133277   22816       3249793     
 250  0.9603210373   53000   15946776179     
 252  0.8886298435   37800   35983220659     
 254  0.7778963787   45974    2545430123     
 256  0.7680769257   53248   12798115129     
 258  0.7684771240   45150  305996132599     
 260  0.7724350668   30160     573522601     
 262  0.8145777421   79386  778033843151     
 264  0.8241313527   46200  313621476739     
 266  0.8801702481   39368     688831433     
 268  0.7914716927   71020  210484888321     
 270  0.9385992389   27000     479487689     
 272  0.7985388488   59568   30497191399     
 274  0.9241529945   68500   13766905759     
 276  0.8452548271   33672    1738757609     
 278  0.8930499724   25854       1925299     
 280  0.7989596541   52360  222398285827     
 282  0.8508107698   23406      32332831     
 284  0.8785941526   66456   12436366727     
 286  0.7858974077   62920  165094766113     
 288  0.7935760257   50688  159328991309     
 290  0.7802020735   65250  737183466337     
 292  0.8835286349   35624      18463427     
 294  0.8874698444   31458     834434033     
 296  0.7407823594   59792   19144263221     
 298  0.8142218681   71520   38040537103     
 300  0.8694555188   31500    1746213839     
 302  0.7889783882   46206     381321631     
 304  0.9026153946   44688     112884059     
 306  0.8374812598   13464        403553     
 308  0.8043192128   57288   38073581723     
 310  0.8496494922   69750  228639573389     
 312  0.8318902760   51168   98393397133     
 314  0.8034115353   51810     676001831     
 316  0.7761217516   36024      30954479     
 318  0.8218376546   39114    1952210459     
 320  0.8298538635   68480  106433008811     
 322  0.8573533053   54740    3560039459     
 324  0.7994627901   61560  394806744763     
 326  0.8083900200   80848   61763668063     
 328  0.7963256514   70848   17418374759     
 330  0.7638121358   28380    2288156501     
 332  0.7948104095   73704   21234656767     
 334  0.7853352422   91850  337046857421     
 336  0.7538847566   48720  185386505651     
 338  0.8637454324   43602      64873867     
 340  0.8240596233   65280   63699574657     
 342  0.8010075672   59850  264946609777     
 344  0.9190160329   66736    1069426291     
 346  0.7997930054   84078   54543153053     
 348  0.8268505391   67512  532187265079     
 350  0.8106891221   61950   91077187501     
 352  0.7785409404   82720  155422575103     
 354  0.8053164792   59826   97833706423     
 356  0.8760991508  102172  151136306521     
 358  0.7782235660   36516      11215003     
 360  0.9190759335   23760      13367671     
 362  0.7574134126   91224  171412985833     
 364  0.7756310715   51324    2040279533     
 366  0.8000166747   25986      13943863     
 368  0.8051615730  105984  753348546229     
 370  0.7987557798   81400  357568042813     
 372  0.7936543460   69192  508077732887     
 374  0.8532053339   58344     951272459     
 376  0.8393024208   62040     506537617     
 378  0.7935133452   61236  406541144927     
 380  0.8062842535   70680   51924372169     
 382  0.7889373294   90916   49616984707     
 384  0.7939465677   43392     941956339     
 386  0.7891241447   86850   24998032091     
 388  0.8235266859   72556    2009863117     
 390  0.7826368919   45240   45380958619     
 392  0.8571708876   75656    9004407101     
 394  0.8099475511   32308       1536583     
 396  0.8578841605   68904  172082709217     
 398  0.8791459095   89152    6737268127     
 400  0.7989545605   12800          9371     
 402  0.7868411869   66732  101933130811     
 404  0.7941196209   83628    9237777071     
 406  0.8585658511   87696   51121166533     
 408  0.8204181763   66912   91749328751     
 410  0.7897091793   46740     225303313     
 412  0.8036159885   90228   15439142689     
 414  0.8961928199   80730  221437110397     
 416  0.8020117468   75296    4013157443     
 418  0.7948806774  102410  415898213609     
 420  0.7627980893   26880     209227433     
 422  0.8690265566   57814      53634703     
 424  0.7602757566   91584   28278509927     
 426  0.7914098117   71994  117628436659     
 428  0.8044283310   40660       5039641     
 430  0.8013985116   55470     653446711     
 432  0.8219377815   53568    1734713993     
 434  0.7722870211  104160  772698979163     
 436  0.8047788797  102896   36828863651     
 438  0.7961083251   57816    5663148871     
 440  0.8792757227   58520     720313157     
 442  0.7596162182   99450  219117304141     
 444  0.9438876646   15984         35257     
 446  0.7775995907   49060      20910913     
 448  0.7848311396   90944   46689332597     
 450  0.7619657101   57600   79481983369     
 452  0.7838385407   97632   17418654119     
 454  0.7682744177  118948  232873806283     
 456  0.8859311160   95304  741680341187     
 458  0.8209257626   71448     305532509     
 460  0.7705031462   72680   11329574903     
 462  0.8277181464   44814    1678178797     
 464  0.8354396498   55680      30933989     
 466  0.8675896733   26562         70937     
 468  0.8983741777   95940  671415930377     
 470  0.8680891345   94000   34320032563     
 472  0.8363640483   66080     103334411     
 474  0.8380885352   81528   69987740731     
 476  0.9122603335   97580   17812528859     
 478  0.8459786783   58316      24551903     
 480  0.8369451486   55200    7215375371     
 482  0.8084758201   85796    1355943101     
 484  0.7928372491   60984     131951387     
 486  0.9670602256   66582     897783067     
 488  0.8040919055  124928  112158744989     
 490  0.8378578846   82320   31813190909     
 492  0.7854804768   93480  699003369871     
 494  0.8392228848   79040    1171149593     
 496  0.7869001503   98704    8483101717     
 498  0.7903333451   86652  169488659107     
 500  0.7914911855  105000  153153439729     
 502  0.9346253968   41164        540139
 504  0.8170280734   50400     974403323
 506  0.8272732557   71852     425671457
 508  0.8267616819  112776   12711671711
 510  0.8611973391   44880     579426871
 512  0.7850984980  121344   46897900787
 514  0.9225813074  174246  625510735951
 516  0.8019834578   72756   12362133493
 518  0.8366088676  101010   18527678629
 520  0.8696185442  109200  127816392311
 522  0.7983405988   46458     120978283
 524  0.8097368830  154580  586125879281
 526  0.8115530554   94680    1460084749
 528  0.8934942692   34848       5998913
 530  0.8049360188   57240     107123117
 532  0.7920246624   30324        575077
 534  0.8161638595   88110   57019930549
 536  0.7799025504  138288  179982795691
 538  0.9016955220  112980    2457304483
 540  0.8029054239   48060     715228027
 542  0.8534940538   61246      11964913
 544  0.8392434214  126208   33574445479
 546  0.8836029793   94458  680726038129
 548  0.8034500145   96996    1410813787
 550  0.7885921427  109450  275839875067
 552  0.7956321590  104880  768279045497
 554  0.7914668223  147364  190546085857
 556  0.8516820096  150676   98958026977
 558  0.9544916211  106020   61428637987
 560  0.7749958441   75040    5660034091
 562  0.7812147343  151740  274490495683
 564  0.8053315904  108852  589938736859
 566  0.7891020079  127916   25853082041
 568  0.8409819101   71568      37194763
 570  0.8015346996   27930       5671207
 572  0.7872642046  100100    9913066937
 574  0.8355665622  104468    8173667093
 576  0.7897361686  103680  227188645297
 578  0.7884091107  106352    4694158901
 580  0.8716154868  135720  282082451569
 582  0.7329439961  103596  607263973321     
 584  0.7923222032  106872    2504438459     
 586  0.8159773780  133608   19239163373     
 588  0.7761971881   58212    1499370799     
 590  0.8344010904  123900   97104120731     
 592  0.9093598272  152736   30757758641     
 594  0.8203596194  103950  333275730829     
 596  0.8752581666  116220    1578834337     
 598  0.7933508876  113022   12263164867     
 600  0.7956697951   19200        196303     
 602  0.8671990408   55986       8882693     
 604  0.8070806533  103284     932676103     
 606  0.7796492138   96960   67559839063     
 608  0.8125159769  141664   48492135667     
 610  0.8365143363   40260       1372451     
 612  0.7978540809   44064      23167169     
 614  0.8275383515   68768      14281613     
 616  0.7562342777  116424   99877977587     
 618  0.8265107359  111240  142939098451     
 620  0.7625254531   44640       6020933     
 622  0.8063729000   93300     245534483     
 624  0.9394014419  132288  577632351979     
 626  0.8003908014  170898  229723986623     
 628  0.8690691013  152604   20089808047     
 630  0.7878195018   83790  635068094299     
 632  0.8457792089  182648  266552475209     
 634  0.8321349317  178154  201487337099     
 636  0.8465112163   94128   11000930573     
 638  0.7538727012   93148    1327646743     
 640  0.9120077454   55040       4602251     
 642  0.8152602768   77040    1475945477     
 644  0.8303242949   97244    1403478863     
 646  0.9148101139  191862  524463691699     
 648  0.8487263784   57024      45602917     
 650  0.7783532479   57850      43857397     
 652  0.8380466032  132356    3876681503     
 654  0.9214740453   51666       9881863     
 656  0.8450147043  194832  454517973809     
 658  0.8049383681  151998  228935733461     
 660  0.8043599214   95700  696335516473     
 662  0.7767298220  179402  308765222369     
 664  0.8497732615  179944  108343097587     
 666  0.9612073070  137196  145879569457     
 668  0.8291122833  161656   33463509787     
 670  0.8588802430  146730  111632773561     
 672  0.8377544361   92064   24553355279     
 674  0.8927385746  154346    7102999643     
 676  0.7911246648   81120      74589533     
 678  0.8188167676  101700   16846380763     
 680  0.7847062189  129880  110374441477     
 682  0.8756801286  157542   43180032209     
 684  0.8371047755   63612     139850671     
 686  0.8425141547  118678    3207660733     
 688  0.7914089252   87376      74464177     
 690  0.8298009290   93150   92923597009     
 692  0.8099695701  189608  213400291319     
 694  0.9352046150  222080  238517976413     
 696  0.8663493208   64728      85359893     
 698  0.7930566851  198930  456923141659     
 700  0.8284455357  136500  239460526523     
 702  0.7511986045   32292       1306499     
 704  0.8202954082  187264  397943965597     
 706  0.8695438095   40242         55201     
 708  0.8977861205  144432  273087013487     
 710  0.7724598204  149810  269015016161     
 712  0.8199108541  213600  652989609751     
 714  0.7953230813  113526  694348824997     
 716  0.7831859227  193320  272750735171     
 718  0.7661030339  186680  214029806201     
 720  0.8760847971  119520  377221918061     
 722  0.7617166259  131404    5674164913     
 724  0.7975329263  110772     339112381     
 726  0.8799338964  137940  391674855421     
 728  0.9518517909  184184  180789356273     
 730  0.8169767948   59130       7609781     
 732  0.8289374951   34404        479797     
 734  0.8603414239  198180   78573408271     
 736  0.7940567828   36064         49669     
 738  0.8187851952   69372     144447397     
 740  0.8024558855  102120    1346388959     
 742  0.8270690786   48972        912367     
 744  0.7697508611  124992  197934069341     
 746  0.8040409658  181278   49168511023     
 748  0.7830564314  139128   17115875771     
 750  0.8359892306  106500   91377216071     
 752  0.7749013078  128592    1668673339     
 754  0.7782240049  183222  313412732261     
 756  0.7984514297   71820     728533909     
 758  0.8307863368  161454    7035777923     
 760  0.8587348951  151240   54915038317     
 762  0.7947601914  132588  149362737379     
 764  0.8072228398  182596   39444378481     
 766  0.8360220240  124092     363645049     
 768  0.8159361794  104448    5146249133     
 770  0.8512445396   80850     435991117     
 772  0.7934001992  214616  336250303541     
 774  0.7963577306   77400     338022701     
 776  0.8694867562   95448      21931331     
 778  0.7896427008  161046    9056973697     
 780  0.7773942238  109200  558379404841     
 782  0.7925574832  168912   48563547259     
 784  0.8187678710   40768        152791     
 786  0.7375163313  128904  182041921063     
 788  0.8598576323  115836     112344431     
 790  0.7449992657  116130    5097460699     
 792  0.7809066212  131472  318121728761     
 794  0.8737191630  146096     839726627     
 796  0.8171350137  216512  171358508429     
 798  0.8189774650  110124   68522931313     
 800  0.7854380237  124000    4429597201     
 802  0.8127895345  231778  394291297993
 804  0.7850960183  134268  113158700561
 806  0.9079408402   82212       7638601
 808  0.7877421483  113120     169209149
 810  0.8116850129   89910    6836640043
 812  0.8851736046  157528    9883553821
 814  0.7938088485  104192     196064567
 816  0.8066643398   61200      29890303
 818  0.8335856530  112884      81576293
 820  0.8731640737   90200      63450923
 822  0.8762643516  110970    2349421741
 824  0.8675619063  149144     821531663
 826  0.7608164263  191632  482975333977
 828  0.7652805026   90252    1510362617
 830  0.9773893526  154380    3391062847
 832  0.8327364626  114816     169459867
 834  0.8070598355   81732     208384291
 836  0.7538505214  174724  104621735923
 838  0.8485627499   66202        791251
 840  0.8015664476   73920    3295891901
 842  0.7876682549   71570       2370917
 844  0.8376720882  181460    7295944001
 846  0.8142049032   83754     242174417
 848  0.8232748309  191648   18770276141
 850  0.9701528945   68850       2865899
 852  0.8246959945   74976      66856927
 854  0.7816720250  118706     831340553
 856  0.8510306674  263648  548615176763
 858  0.7730683037   55770      33794983
 860  0.7875830400  184040  283849393787
 862  0.7629563985  160332    3988841561
 864  0.8914155653   49248        986113
 866  0.7871098852  122972     181431827
 868  0.7913892342  123256    1079341177
 870  0.8374583079   82650    1305824189
 872  0.7561328839  190968   31683162491
 874  0.7722875504  180044   34472439539
 876  0.8255392548  135780   23908792657
 878  0.8059992615  178234    5732050237
 880  0.8181553201  134640    7058010781
 882  0.8094486988   98784    3607715213
 884  0.7567896075  177684   54800797889
 886  0.8355161599  239220  113074220731
 888  0.8258816962  101232     911045519
 890  0.8369225223  100570     105642601
 892  0.7741629232  202484   34734355067
 894  0.8349591749   82248      83596313
 896  0.8173757133  190848   51175902559
 898  0.7948385029  204744   25932816499
 900  0.8072861180  135000  290994718649
 902  0.8232989477  217382  143887883981
 904  0.7813795699  218768   71929518179
 906  0.8341247493  126840    5993514403
 908  0.8038721784  124396     108448177
 910  0.8725257404   66430      11447977     
 912  0.7475902881  153216  384881446787     
 914  0.7934699183  232156  100197840751     
 916  0.8514071759  204268    9155647951     
 918  0.8050224606  136782   35374365181     
 920  0.8424586115   61640       1763849     
 922  0.7601528076  214826   58158071267     
 924  0.8530073203   69300      97746161     
 926  0.8116795701  221314   35526795583     
 928  0.8150834574  208800   24269915627     
 930  0.9064778846   68820      52930403     
 932  0.8943236869  212496    6725412643     
 934  0.9991973371  137298      28542649     
 936  0.8676912530   71136      21181103     
 938  0.8053687523  217616  221046403007     
 940  0.8089099343  177660   40714396309     
 942  0.8067961396   87606     126384917     
 944  0.8331691839  189744    4182919339     
 946  0.9314959033  290422  680302968469     
 948  0.8534806884  193392  505670821001     
 950  0.8545569452  122550     465470219     
 952  0.8405042747  119952     235628287     
 954  0.8998573515   60102       2200661     
 956  0.7626024207  247604  220062550277     
 958  0.8529434109  214592    9196163681     
 960  0.8904686989  120960   10093588667     
 962  0.8144970096   88504       7634353     
 964  0.8004216214  107004      17584639     
 966  0.8283176903  122682   19348856179     
 968  0.9204665049  279752  259460206361     
 970  0.8013154534  204670  158734118899     
 972  0.8225551898  150660   21178988759     
 974  0.8534921688  303888  568872068111     
 976  0.9105943329  278160   90346489859     
 978  0.7903996503  165282  107942471909     
 980  0.7846347168  117600    1487302123     
 982  0.8063698833  262194  153969081667     
 984  0.7799444190  169248  203888107831     
 986  0.7924196264  225794   89694739373     
 988  0.8062837244  204516   33384442471     
 990  0.7913342257   97020    6544493717     
 992  0.8327256129  248000   65733837647     
 994  0.8168423482  217686   87037919861     
 996  0.8046526420   66732       7982237     
 998  0.8287134801  212574    7185918043     
1000  0.8366128339  192000   25270575311     

current record for CSG_max with 1000 < q <= 2690: 0.9937793256 @ q=1236
I begin to wonder - a lot of people look for a run of consecutive primes in AP, but hardly anyone considered the prime gaps??
(Gaps in AP - GAP, so to speak)

Last fiddled with by mart_r on 2020-04-30 at 15:10
mart_r is offline   Reply With Quote
Old 2020-05-01, 08:51   #15
mart_r
 
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Dec 2008
you know...around...

25·19 Posts
Default

Here's something that may or may not be interesting:
Code:
Analysis max. CSG values for each q<=1000,
after p is searched to a given point:
 
p <=       minimum       maximum   average (Ø)        median
2^10  0.2804444784  0.6807107024  0.4161595621  0.4064414965
2^11  0.3153140952  0.8163798773  0.4479011102  0.4381184715
2^12  0.3431763163  0.8163798773  0.4810577367  0.4669620236
2^13  0.3639186774  0.8469687305  0.5106163332  0.4937025305
2^14  0.4015493440  0.8469687305  0.5417778504  0.5299481585
2^15  0.4292063878  0.8469687305  0.5679300130  0.5598621739
2^16  0.4455266020  0.9438876646  0.6019060399  0.5953644060
2^17  0.4955019575  0.9438876646  0.6276172592  0.6182244977
2^18  0.5136449268  0.9438876646  0.6494452049  0.6377217355
2^19  0.5344779917  0.9438876646  0.6652764872  0.6565675064
2^20  0.5613913893  0.9438876646  0.6814686201  0.6716402626
2^21  0.5715141585  0.9438876646  0.6937490856  0.6821047684
2^22  0.5774364852  0.9701528945  0.7080072985  0.6979367005
2^23  0.5862470282  0.9701528945  0.7194394574  0.7085265144
2^24  0.6158419682  0.9701528945  0.7301409005  0.7173491757
2^25  0.6173926504  0.9991973371  0.7415097777  0.7277374372
2^26  0.6188545442  0.9991973371  0.7497651120  0.7389833874
2^27  0.6592723517  0.9991973371  0.7577502171  0.7486021715
2^28  0.6600619545  0.9991973371  0.7651549239  0.7561863044
2^29  0.6759517875  0.9991973371  0.7723897323  0.7643196755
2^30  0.6759517875  0.9991973371  0.7783479756  0.7697527744
2^31  0.6761477729  0.9991973371  0.7835304099  0.7755264553
2^32  0.6834157728  0.9991973371  0.7891625626  0.7816272396
2^33  0.6938642847  0.9991973371  0.7947508404  0.7869154610
2^34  0.6987121002  0.9991973371  0.7987109313  0.7889756907
2^35  0.7122729187  0.9991973371  0.8041287036  0.7946700265
2^36  0.7122729187  0.9991973371  0.8087488394  0.8009100665
2^37  0.7212478685  0.9991973371  0.8125613682  0.8043811238
2^38  0.7289731501  0.9991973371  0.8180076512  0.8069279875
2^39  0.7289731501  0.9991973371  0.8215276632  0.8121152514

8e11  0.7329439961  0.9991973371  0.8239166643  0.8152880248
One of the questions is: Are all q unbiased for CSG_max - i.e. will the values for average and median stay roughly the same if larger q are taken into account?
For me, it's natural to compare q=30*m for m<=33 here: 22 values are below, 11 above median total; the average of q=30*m for m<=33 at 2^39 is below the average total at 2^38, so at first glance not quite convincing: There seems to be a bias toward that q=2*prime have a higher probability to have CSG_max above median and q=6*m or q=30*m for integer m have a higher probability to have CSG_max below median - BUT only for small q, say q<200 or thereabouts. For higher q, the bias seems no longer present. I shall make the same analysis in smaller clusters of q and check how average and median behaves, later.


Here's how the story might continue:
Code:
p <=         log p           z-Ø for z=0.9721
2^10  6.9314718056  0.5559404379
2^11  7.6246189862  0.5241988898
2^12  8.3177661667  0.4910422633
2^13  9.0109133473  0.4614836668
2^14  9.7040605278  0.4303221496
2^15  10.397207708  0.4041699870
2^16  11.090354889  0.3701939601
2^17  11.783502070  0.3444827408
2^18  12.476649250  0.3226547951
2^19  13.169796431  0.3068235128
2^20  13.862943611  0.2906313799
2^21  14.556090792  0.2783509144
2^22  15.249237972  0.2640927015
2^23  15.942385153  0.2526605426
2^24  16.635532333  0.2419590995
2^25  17.328679514  0.2305902223
2^26  18.021826695  0.2223348880
2^27  18.714973875  0.2143497829
2^28  19.408121056  0.2069450761
2^29  20.101268236  0.1997102677
2^30  20.794415417  0.1937520244
2^31  21.487562597  0.1885695901
2^32  22.180709778  0.1829374374
2^33  22.873856958  0.1773491596
2^34  23.567004139  0.1733890687
2^35  24.260151320  0.1679712964
2^36  24.953298500  0.1633511606
2^37  25.646445681  0.1595386318
2^38  26.339592861  0.1540923488
2^39  27.032740042  0.1505723368
Here, z=0.9721 gives a reciprocal regression line (see attachment "reciprocal regression") in the sense that log p ~ 4.052*(z-Ø)^-1. Although it doesn't fit perfectly, it's quite close. I might try it again using values of q<=2000.

This may or may not suggest that the average CSG_max values converge to a value less than 1, and furthermore that the number of gaps > \varphi*log²p might be finite for each q. But the amount of data is not asymptotic to the amount of proof...

For other values of z, the line fits less good. Anyway, for the thrill of it, some values of z and how the coefficients A and B in the regression log p ~ A*(z-Ø)^B behaves:
Code:
   z       A        B
0.95  4.1486  -0.9168
0.96  4.1003  -0.9546
0.97  4.0597  -0.9921
0.98  4.0260  -1.0292
0.99  3.9986  -1.0661
1.00  3.9770  -1.1026
It gets quite impressive when dealing with log p vs. 1/(z-Ø). Here the regression becomes eerily linear when z=0.97125 (note that this is a bit less than the z used for the reciprocal regression). I let the graph in the attachment speak for itself, with the additional note that the top right point there is the data for 8e11, all others are for 2^n with 10 <= n <= 39 - and no, that's not the reason why this z is a little smaller.

Suggestion to myself: try if the values, especially for the smaller p, fit a little better when using Sum[Ri'(x)] for CSG.


I'm full of ideas right now, just not sure if I'm heading in the right direction.
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Last fiddled with by mart_r on 2020-05-01 at 09:12 Reason: derivative of derivative is abundant:)
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Old 2020-05-09, 11:46   #16
mart_r
 
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Dec 2008
you know...around...

25×19 Posts
Default Results p<10^12

Data as of 2020-05-04, all p<1012 for q<=1000 have been searched:
Code:
q: common difference in arithmetic progression p+k*q
CSG: Cramér-Shanks-Granville ratio via gap/phi(q)/log(p+gap)²
CSG_max: maximum value found for CSG up to p=10^12
p: prime preceding the gap

current record for CSG_max: 1.0010143609 @ q=152

   q  CSG_max          gap             p
   2  0.7953486740     456   25056082087
   4  0.8056652398    1044  113391385573
   6  0.7541322181     462      39895309
   8  0.7875867918    2080  144309631099
  10  0.8930327253    2450  236455710509
  12  0.8455173596    2352  283661812859
  14  0.8345982115    2884   26448217657
  16  0.9046153418    3728    7194688583
  18  0.7887450235     702        194027
  20  0.7944296249    1600       7775737
  22  0.8617839921    2002       4160719
  24  0.8117145259    4392  197036728351
  26  0.8652413900    7540  505084610521
  28  0.9062903537    8232  888138723221
  30  0.8058232068    1980      40846943
  32  0.8965150715    3808      11911369
  34  0.8182937153    3876      29673503
  36  0.7872577337    5400   24166901071
  38  0.8518980455    2280        195271
  40  0.8613707321   10440  897576340499
  42  0.8251402679    3780     305816297
  44  0.8085714112   11132  248049290057
  46  0.8034522392    7268     640376543
  48  0.7973452005    7344   26302298977
  50  0.8793539278    4950      19315399
  52  0.7811165997   13832  626287370141
  54  0.7956494153    7344    6831679457
  56  0.8531838024   13272  113946560627
  58  0.8160213701   17052  731647597039
  60  0.7594431944    8760  457941678127
  62  0.7505368847   16740  694602632629
  64  0.8613806693    7104       9370547
  66  0.7637963086    9834  104493100477
  68  0.7981407159   13056    6594265703
  70  0.8282785007   11900   42252957959
  72  0.8602785358    4824       4344187
  74  0.9131005021    9620      26876579
  76  0.8416067457   16796   16804480523
  78  0.7510340136    9828   13836158729
  80  0.8244076217   19680  727457191561
  82  0.8163798773    2214          1553
  84  0.8017445129   11172   29153099231
  86  0.8236614027    9718      19002559
  88  0.8173745127   22528  251192223571
  90  0.7978827104   14580  962979692377
  92  0.8569074437   19320    6775293947
  94  0.7540215308   21244   55988532973
  96  0.7963941131   17280  203618303897
  98  0.8195247347   12936     262621343
 100  0.7442402852   20600  265671964073
 102  0.7887967496   16626  139972076507
 104  0.9499776231   31200  229169128997
 106  0.9015411061   33072  342820240309
 108  0.8456207760   20196  153489937273
 110  0.7957899312   21780  229165433009
 112  0.8754122474   19376    2117717087
 114  0.8493019884   22116  478998886567
 116  0.7977964383   32248  465563693299
 118  0.8167041620   20886    1316371417
 120  0.8057216311   14040   13628678729
 122  0.7947909820   28182   36113593211
 124  0.8316652784   30628   57483096991
 126  0.9142860299   18270   17061510127
 128  0.8323761564    7296        113623
 130  0.7938556043   21450   20138027813
 132  0.7846464407   10560      92494289
 134  0.8397671201   14740      12075073
 136  0.7672983613   26928   14785702759
 138  0.7924769327   15042    1047660137
 140  0.9112585981   31360  425297500759
 142  0.8610872285   43026  401037154541
 144  0.7893617069   17856    2678906773
 146  0.8196507109   23652     494696261
 148  0.7830010017   42328  794519516383
 150  0.7557605255   21000  279561600257
 152  1.0010143609   54264  825353008489
 154  0.9369830338   35728   88779374809
 156  0.7985008265   13728     165640219
 158  0.7606501324   43134  512782039607
 160  0.8211887580   36960  328840371359
 162  0.8258805846   26244   34294519837
 164  0.7924402630   47232  714913847737
 166  0.8175587888   42828   94831438649
 168  0.7739486136   24864  171996125029
 170  0.7905258192   29240   27579604799
 172  0.8745407940   38356    8387732083
 174  0.8966388328   14616      25666717
 176  0.8893387228   32912    2191630061
 178  0.7718247316   44856  144798233893
 180  0.7968104593   22680   37641351263
 182  0.8820202987   27482    1082590961
 184  0.8892744577   56856  508307558683
 186  0.8021152848   15624      66824477
 188  0.7964246226   40044   14217429113
 190  0.8735201597   38950   64231886011
 192  0.8583746127   11904       2459623
 194  0.8234255916   44232   18757576997
 196  0.8703957715   44100   46355125469
 198  0.7511941018   20196    1560142237
 200  0.8255106246   39800   45870059471
 202  0.8455991259   26462      48134069
 204  0.8383878988   31212   29818321129
 206  0.8849004882   20806       3903223
 208  0.8637254761   47008   21908990083
 210  0.7941670680   27510  464338653979
 212  0.8726800198   57028   76983450889
 214  0.8300985533   54570   65376711233
 216  0.8565309700   38016   60639375773
 218  0.8025184444   64746  741341656273
 220  0.8516677011   11220        363019
 222  0.7476242389   35964  168120545239
 224  0.7530876774   27552     300702751
 226  0.8205657931   65314  378168298933
 228  0.7687388396   35568  102156515693
 230  0.8278708905   49910  232943726651
 232  0.7860150605   25288      22918543
 234  0.7932876948   27144    2934877793
 236  0.9437796854   79296  487692833143
 238  0.7961571214   47838   73308073691
 240  0.8040958748   37680  564376543243
 242  0.8312839360   32912     173468021
 244  0.8153157728   64172  132595555181
 246  0.8801251829   47478  189457586089
 248  0.8449133277   22816       3249793
 250  0.9603210373   53000   15946776179
 252  0.8886298435   37800   35983220659
 254  0.7778963787   45974    2545430123
 256  0.7699134788   74496  872095415663
 258  0.7684771240   45150  305996132599
 260  0.7724350668   30160     573522601
 262  0.8145777421   79386  778033843151
 264  0.8241313527   46200  313621476739
 266  0.8801702481   39368     688831433
 268  0.7914716927   71020  210484888321
 270  0.9385992389   27000     479487689
 272  0.7985388488   59568   30497191399
 274  0.9241529945   68500   13766905759
 276  0.8452548271   33672    1738757609
 278  0.8930499724   25854       1925299
 280  0.7989596541   52360  222398285827
 282  0.8508107698   23406      32332831
 284  0.8785941526   66456   12436366727
 286  0.7858974077   62920  165094766113
 288  0.7935760257   50688  159328991309
 290  0.7943100395   67570  931070381161
 292  0.8835286349   35624      18463427
 294  0.8874698444   31458     834434033
 296  0.7407823594   59792   19144263221
 298  0.8142218681   71520   38040537103
 300  0.8694555188   31500    1746213839
 302  0.7889783882   46206     381321631
 304  0.9026153946   44688     112884059
 306  0.8374812598   13464        403553
 308  0.8043192128   57288   38073581723
 310  0.8496494922   69750  228639573389
 312  0.8318902760   51168   98393397133
 314  0.8034115353   51810     676001831
 316  0.7761217516   36024      30954479
 318  0.8218376546   39114    1952210459
 320  0.8298538635   68480  106433008811
 322  0.8573533053   54740    3560039459
 324  0.7994627901   61560  394806744763
 326  0.8083900200   80848   61763668063
 328  0.7963256514   70848   17418374759
 330  0.7638121358   28380    2288156501
 332  0.7948104095   73704   21234656767
 334  0.7993791033  100200  859105770221
 336  0.7538847566   48720  185386505651
 338  0.8637454324   43602      64873867
 340  0.8240596233   65280   63699574657
 342  0.8010075672   59850  264946609777
 344  0.9190160329   66736    1069426291
 346  0.7997930054   84078   54543153053
 348  0.8268505391   67512  532187265079
 350  0.8106891221   61950   91077187501
 352  0.7785409404   82720  155422575103
 354  0.8053164792   59826   97833706423
 356  0.8760991508  102172  151136306521
 358  0.7782235660   36516      11215003
 360  0.9190759335   23760      13367671
 362  0.7879479541  108238  994159631581
 364  0.7756310715   51324    2040279533
 366  0.8000166747   25986      13943863
 368  0.8051615730  105984  753348546229
 370  0.7987557798   81400  357568042813
 372  0.7936543460   69192  508077732887
 374  0.8532053339   58344     951272459
 376  0.8393024208   62040     506537617
 378  0.7935133452   61236  406541144927
 380  0.8062842535   70680   51924372169
 382  0.7889373294   90916   49616984707
 384  0.7939465677   43392     941956339
 386  0.7891241447   86850   24998032091
 388  0.8235266859   72556    2009863117
 390  0.7826368919   45240   45380958619
 392  0.8571708876   75656    9004407101
 394  0.8099475511   32308       1536583
 396  0.8578841605   68904  172082709217
 398  0.8791459095   89152    6737268127
 400  0.7989545605   12800          9371
 402  0.7868411869   66732  101933130811
 404  0.7941196209   83628    9237777071
 406  0.8585658511   87696   51121166533
 408  0.8204181763   66912   91749328751
 410  0.7897091793   46740     225303313
 412  0.8036159885   90228   15439142689
 414  0.8961928199   80730  221437110397
 416  0.8020117468   75296    4013157443
 418  0.7948806774  102410  415898213609
 420  0.7627980893   26880     209227433
 422  0.8690265566   57814      53634703
 424  0.7734492416  121688  879624723533
 426  0.8161742410   86052  828253660439
 428  0.8044283310   40660       5039641
 430  0.8013985116   55470     653446711
 432  0.8219377815   53568    1734713993
 434  0.7722870211  104160  772698979163
 436  0.8047788797  102896   36828863651
 438  0.7961083251   57816    5663148871
 440  0.8792757227   58520     720313157
 442  0.7596162182   99450  219117304141
 444  0.9438876646   15984         35257
 446  0.7775995907   49060      20910913
 448  0.7848311396   90944   46689332597
 450  0.7619657101   57600   79481983369
 452  0.7838385407   97632   17418654119
 454  0.7682744177  118948  232873806283
 456  0.8859311160   95304  741680341187
 458  0.8209257626   71448     305532509
 460  0.7705031462   72680   11329574903
 462  0.8277181464   44814    1678178797
 464  0.8354396498   55680      30933989
 466  0.8675896733   26562         70937
 468  0.8983741777   95940  671415930377
 470  0.8680891345   94000   34320032563
 472  0.8363640483   66080     103334411
 474  0.8380885352   81528   69987740731
 476  0.9122603335   97580   17812528859
 478  0.8459786783   58316      24551903
 480  0.8369451486   55200    7215375371
 482  0.8084758201   85796    1355943101
 484  0.7928372491   60984     131951387
 486  0.9670602256   66582     897783067
 488  0.8236013888  148840  826719013189
 490  0.8378578846   82320   31813190909
 492  0.7854804768   93480  699003369871
 494  0.8392228848   79040    1171149593
 496  0.7869001503   98704    8483101717
 498  0.7903333451   86652  169488659107
 500  0.7914911855  105000  153153439729
 502  0.9346253968   41164        540139
 504  0.8170280734   50400     974403323
 506  0.8272732557   71852     425671457
 508  0.8267616819  112776   12711671711
 510  0.8611973391   44880     579426871
 512  0.7850984980  121344   46897900787
 514  0.9225813074  174246  625510735951
 516  0.8019834578   72756   12362133493
 518  0.8366088676  101010   18527678629
 520  0.8696185442  109200  127816392311
 522  0.7983405988   46458     120978283
 524  0.8097368830  154580  586125879281
 526  0.8460548204  168846  968617929451
 528  0.8934942692   34848       5998913
 530  0.8049360188   57240     107123117
 532  0.7920246624   30324        575077
 534  0.8161638595   88110   57019930549
 536  0.7799025504  138288  179982795691
 538  0.9016955220  112980    2457304483
 540  0.8029054239   48060     715228027
 542  0.8534940538   61246      11964913
 544  0.8392434214  126208   33574445479
 546  0.8836029793   94458  680726038129
 548  0.8034500145   96996    1410813787
 550  0.7885921427  109450  275839875067
 552  0.7956321590  104880  768279045497
 554  0.7914668223  147364  190546085857
 556  0.8516820096  150676   98958026977
 558  0.9544916211  106020   61428637987
 560  0.7749958441   75040    5660034091
 562  0.7812147343  151740  274490495683
 564  0.8053315904  108852  589938736859
 566  0.7891020079  127916   25853082041
 568  0.8409819101   71568      37194763
 570  0.8015346996   27930       5671207
 572  0.7872642046  100100    9913066937
 574  0.8355665622  104468    8173667093
 576  0.7897361686  103680  227188645297
 578  0.7884091107  106352    4694158901
 580  0.8716154868  135720  282082451569
 582  0.7329439961  103596  607263973321
 584  0.7923222032  106872    2504438459
 586  0.8159773780  133608   19239163373
 588  0.7761971881   58212    1499370799
 590  0.8344010904  123900   97104120731
 592  0.9093598272  152736   30757758641
 594  0.8203596194  103950  333275730829
 596  0.8752581666  116220    1578834337
 598  0.7972637502  159068  869224163201
 600  0.7956697951   19200        196303
 602  0.8671990408   55986       8882693
 604  0.8070806533  103284     932676103
 606  0.7796492138   96960   67559839063
 608  0.8125159769  141664   48492135667
 610  0.8365143363   40260       1372451
 612  0.7978540809   44064      23167169
 614  0.8275383515   68768      14281613
 616  0.7562342777  116424   99877977587
 618  0.8265107359  111240  142939098451
 620  0.7625254531   44640       6020933
 622  0.8063729000   93300     245534483
 624  0.9394014419  132288  577632351979
 626  0.8240605983  195312  933121023811
 628  0.8690691013  152604   20089808047
 630  0.7878195018   83790  635068094299
 632  0.8457792089  182648  266552475209
 634  0.8321349317  178154  201487337099
 636  0.8465112163   94128   11000930573
 638  0.7538727012   93148    1327646743
 640  0.9120077454   55040       4602251
 642  0.8152602768   77040    1475945477
 644  0.8303242949   97244    1403478863
 646  0.9148101139  191862  524463691699
 648  0.8487263784   57024      45602917
 650  0.7783532479   57850      43857397
 652  0.8380466032  132356    3876681503
 654  0.9214740453   51666       9881863
 656  0.8450147043  194832  454517973809
 658  0.8049383681  151998  228935733461
 660  0.8043599214   95700  696335516473
 662  0.7812198551  195952  940473435469
 664  0.8497732615  179944  108343097587
 666  0.9612073070  137196  145879569457
 668  0.8291122833  161656   33463509787
 670  0.8588802430  146730  111632773561
 672  0.8377544361   92064   24553355279
 674  0.8927385746  154346    7102999643
 676  0.7911246648   81120      74589533
 678  0.8188167676  101700   16846380763
 680  0.7847062189  129880  110374441477
 682  0.8756801286  157542   43180032209
 684  0.8371047755   63612     139850671
 686  0.8425141547  118678    3207660733
 688  0.7914089252   87376      74464177
 690  0.8298009290   93150   92923597009
 692  0.8099695701  189608  213400291319
 694  0.9352046150  222080  238517976413
 696  0.8663493208   64728      85359893
 698  0.7930566851  198930  456923141659
 700  0.8284455357  136500  239460526523
 702  0.9106053914  148122  827875560931
 704  0.8202954082  187264  397943965597
 706  0.8695438095   40242         55201
 708  0.8977861205  144432  273087013487
 710  0.7724598204  149810  269015016161
 712  0.8199108541  213600  652989609751
 714  0.7953230813  113526  694348824997
 716  0.7831859227  193320  272750735171
 718  0.7661030339  186680  214029806201
 720  0.8760847971  119520  377221918061
 722  0.7724554548  201438  982598073973
 724  0.7975329263  110772     339112381
 726  0.8799338964  137940  391674855421
 728  0.9518517909  184184  180789356273
 730  0.8169767948   59130       7609781
 732  0.8289374951   34404        479797
 734  0.8603414239  198180   78573408271
 736  0.7940567828   36064         49669
 738  0.8187851952   69372     144447397
 740  0.9215487467  202020  959204145013
 742  0.8270690786   48972        912367
 744  0.7697508611  124992  197934069341
 746  0.8040409658  181278   49168511023
 748  0.7830564314  139128   17115875771
 750  0.8359892306  106500   91377216071
 752  0.7749013078  128592    1668673339
 754  0.7901283265  199810  821226058453
 756  0.7984514297   71820     728533909
 758  0.8307863368  161454    7035777923
 760  0.8587348951  151240   54915038317
 762  0.7947601914  132588  149362737379
 764  0.8072228398  182596   39444378481
 766  0.8360220240  124092     363645049
 768  0.8159361794  104448    5146249133
 770  0.8561631304  154770  830060466467
 772  0.7934001992  214616  336250303541
 774  0.7963577306   77400     338022701
 776  0.8694867562   95448      21931331
 778  0.7896427008  161046    9056973697
 780  0.7773942238  109200  558379404841
 782  0.7925574832  168912   48563547259
 784  0.8187678710   40768        152791
 786  0.7375163313  128904  182041921063
 788  0.8598576323  115836     112344431
 790  0.7632748154  179330  827400226427
 792  0.7809066212  131472  318121728761
 794  0.8737191630  146096     839726627
 796  0.8171350137  216512  171358508429
 798  0.8189774650  110124   68522931313
 800  0.7854380237  124000    4429597201
 802  0.8127895345  231778  394291297993
 804  0.7850960183  134268  113158700561
 806  0.9079408402   82212       7638601
 808  0.7877421483  113120     169209149
 810  0.8116850129   89910    6836640043
 812  0.8851736046  157528    9883553821
 814  0.7938088485  104192     196064567
 816  0.8066643398   61200      29890303
 818  0.8335856530  112884      81576293
 820  0.8731640737   90200      63450923
 822  0.8762643516  110970    2349421741
 824  0.8675619063  149144     821531663
 826  0.7608164263  191632  482975333977
 828  0.7652805026   90252    1510362617
 830  0.9773893526  154380    3391062847
 832  0.8327364626  114816     169459867
 834  0.8070598355   81732     208384291
 836  0.7538505214  174724  104621735923
 838  0.8485627499   66202        791251
 840  0.8015664476   73920    3295891901
 842  0.7876682549   71570       2370917
 844  0.8376720882  181460    7295944001
 846  0.8142049032   83754     242174417
 848  0.8232748309  191648   18770276141
 850  0.9701528945   68850       2865899
 852  0.8246959945   74976      66856927
 854  0.7816720250  118706     831340553
 856  0.8510306674  263648  548615176763
 858  0.7730683037   55770      33794983
 860  0.8197281512  208980  917866963313
 862  0.7629563985  160332    3988841561
 864  0.8914155653   49248        986113
 866  0.7871098852  122972     181431827
 868  0.7913892342  123256    1079341177
 870  0.8374583079   82650    1305824189
 872  0.7561328839  190968   31683162491
 874  0.7722875504  180044   34472439539
 876  0.8255392548  135780   23908792657
 878  0.8059992615  178234    5732050237
 880  0.8181553201  134640    7058010781
 882  0.8094486988   98784    3607715213
 884  0.7567896075  177684   54800797889
 886  0.8355161599  239220  113074220731
 888  0.8258816962  101232     911045519
 890  0.8369225223  100570     105642601
 892  0.7741629232  202484   34734355067
 894  0.8349591749   82248      83596313
 896  0.8173757133  190848   51175902559
 898  0.7948385029  204744   25932816499
 900  0.8072861180  135000  290994718649
 902  0.8232989477  217382  143887883981
 904  0.7813795699  218768   71929518179
 906  0.8341247493  126840    5993514403
 908  0.8038721784  124396     108448177
 910  0.8725257404   66430      11447977
 912  0.7593864429  166896  993555184957
 914  0.7934699183  232156  100197840751
 916  0.8514071759  204268    9155647951
 918  0.8050224606  136782   35374365181
 920  0.8424586115   61640       1763849
 922  0.7601528076  214826   58158071267
 924  0.8530073203   69300      97746161
 926  0.8116795701  221314   35526795583
 928  0.8150834574  208800   24269915627
 930  0.9064778846   68820      52930403
 932  0.8943236869  212496    6725412643
 934  0.9991973371  137298      28542649
 936  0.8676912530   71136      21181103
 938  0.8053687523  217616  221046403007
 940  0.8630893831  239700  852543477769
 942  0.8067961396   87606     126384917
 944  0.8331691839  189744    4182919339
 946  0.9314959033  290422  680302968469
 948  0.8534806884  193392  505670821001
 950  0.8545569452  122550     465470219
 952  0.8405042747  119952     235628287
 954  0.8998573515   60102       2200661
 956  0.7626024207  247604  220062550277
 958  0.8529434109  214592    9196163681
 960  0.8904686989  120960   10093588667
 962  0.8144970096   88504       7634353
 964  0.8004216214  107004      17584639
 966  0.8283176903  122682   19348856179
 968  0.9204665049  279752  259460206361
 970  0.8013154534  204670  158734118899
 972  0.8225551898  150660   21178988759
 974  0.8534921688  303888  568872068111
 976  0.9105943329  278160   90346489859
 978  0.7903996503  165282  107942471909
 980  0.7846347168  117600    1487302123
 982  0.8063698833  262194  153969081667
 984  0.7799444190  169248  203888107831
 986  0.7924196264  225794   89694739373
 988  0.8062837244  204516   33384442471
 990  0.7913342257   97020    6544493717
 992  0.8327256129  248000   65733837647
 994  0.8168423482  217686   87037919861
 996  0.8046526420   66732       7982237
 998  0.8287134801  212574    7185918043
1000  0.8366128339  192000   25270575311

current record for CSG_max with 1000 < q <= 2690: 0.9961616621 / p=131264869717 @ q=1502
In subsequent updates, I'll only post new results for p>1012.

New code in the attachment, if anyone wants to check if I'm doing things right.
(Ponder this: why is the search slower when the interval is larger? When I use v& = 250*106, it takes more time per q per 1e9 than with e.g. v& = 100*106.)
Attached Files
File Type: zip results_all_10^12.zip (689.2 KB, 103 views)
File Type: txt PGAP_code.txt (4.8 KB, 76 views)
mart_r is offline   Reply With Quote
Old 2020-05-23, 12:57   #17
mart_r
 
mart_r's Avatar
 
Dec 2008
you know...around...

25·19 Posts
Default An update before a long weekend

Just letting you know, I'm still on it.

All q<=2690 have now also been searched to p<1012.
For q<=1000, only new results for 1012<p<3*1012 are shown in the table.
Code:
q: common difference in arithmetic progression p+k*q
CSG: Cramér-Shanks-Granville ratio via gap/phi(q)/log(p+gap)²
CSG_max: maximum value found for CSG up to p=3*10^12 for q<=1000
                                 and up to p=1*10^12 for 1002<=q<=2690
p: prime preceding the gap

current record for CSG_max: 1.0010143609 @ q=152

   q  CSG_max          gap              p
   2  0.7975364451     652  2614941710599
   4  0.8156352348    1296  1742590107893
   6  0.8043096326    1302  2267675747429
  36  0.7953959798    7776  2488620283151
  44  0.8161839043   13024  1850366919097
  52  0.8552310627   16588  2219314413889
  60  0.7669174562   10020  2572440924871
  78  0.7743337878   14430  1263973956209
  96  0.8182152357   20448  1369965278489
 100  0.7680513916   23700  1154488219009
 108  0.8602004012   24840  1995773049461
 120  0.8282174817   21720  2708602511759
 132  0.7859399899   25080  1847468163427
 144  0.8107023756   31248  2026608933563
 164  0.8441634292   51988  1121341862779
 168  0.8433419790   31080  1080904914041
 188  0.8027478817   58468  1658375170513
 204  0.8539893393   41820  1030953050879
 222  0.7849812426   46398  2775690916351
 228  0.7808534284   46056  2692471834747
 256  0.7763078423   81408  2695929230861
 260  0.8048824266   61100  1631014483229
 296  0.8053960245   92056  1720183292131
 316  0.7812949989   99856  2696940430573
 320  0.8711507167   87360  1432030776599
 324  0.8811825528   78408  2922713649013
 332  0.8098772215  106572  2004292884031
 336  0.7795787395   58800  1490297805131
 354  0.8154566619   73278  1223614030909
 362  0.8103149561  119098  2570663585143
 378  0.7960964800   68796  1927024584677
 382  0.7974241509  123768  2586552507463
 400  0.8031013151  104800  2528142047017
 404  0.8092199728  132512  2672534840891
 410  0.8104490914  104550  2146419881959
 420  0.8137078518   63840  2602583597491
 424  0.7942461165  129744  1481798051813
 426  0.8289323077   93720  2196617261591
 442  0.7598300383  119782  2781776304577
 446  0.8458889929  144058  1068393787429
 460  0.7789301939  106260  1233214813793
 464  0.8572536024  146624  1001714625503
 482  0.8414206048  161470  1907903025913
 496  0.8681833256  167648  2084041939613
 518  0.8616203249  146076  1469437363843
 524  0.8373313497  172920  1736690999713
 560  0.8286810737  131040  2907735010097
 562  0.8012678143  183774  2689292102213
 570  0.8077786761   90630  1325924145547
 606  0.7832381303  129078  2928289981961
 614  0.8278175055  206304  2477198425619
 630  0.8008557008   90090  1375553927617
 638  0.7613227599  168432  1613175082811
 658  0.8130657611  173712  1211146285927
 700  0.8448666880  156100  1121946737221
 716  0.8167618692  234848  2200662519749
 730  0.8354837675  190530  1662765783331
 736  0.8188024802  228896  1733418109697
 738  0.8397515047  158670  1533579302309
 752  0.8198735059  245152  2396322870481
 764  0.8457379887  249828  1284203453959
 772  0.8407408933  247812  1077217612519
 774  0.8133175100  162540  1699086152611
 776  0.9050703906  277032  1825864325267
 786  0.7769364381  162702  2115479982437
 788  0.8655999552  274224  2219521221103
 792  0.7890711683  149688  1621645314451
 806  0.9415866545  259532  1040072922719
 828  0.8617772785  182988  2073720212383
 836  0.7607113183  216524  1628172420059
 842  0.8318604579  268598  1100638524959
 844  0.8385676885  288648  2710003170233
 872  0.8379003012  284272  1481278956049
 874  0.8527915219  262200  1262666597447
 878  0.8268563093  293252  2281019340629
 896  0.8323652240  261632  2662613002121
 912  0.7999319242  180576  1441530403283
 918  0.8142665500  182682  1322501588087
 922  0.8143471563  291352  1293675650599
 926  0.8700093869  316692  1550438309309
 954  0.9313516973  224190  1156330148921
 972  0.8329651188  218700  2306583801539
 980  0.8321288844  223440  1893277237571
 982  0.8406561335  332898  2219125353463
 984  0.7883655576  201720  1908143874971
 998  0.8542800442  331336  1318358219977

1002  0.8173324542  101202      243721099
1004  0.9335109890  277104    38179649843
1006  0.7986257468  205224     6697982497
1008  0.8180657107   89712      298174159
1010  0.8102755199  164630     6136972889
1012  0.8469913079  273240   574841273183
1014  0.8057706816   53742        2183809
1016  0.7778067456  252984   107806726613
1018  0.8263188853  293184   300287895043
1020  0.8381299562   79560      230533159
1022  0.7867645035  194180    24021101957
1024  0.9585073790  104448        2062273
1026  0.9039253698  179550    56651445803
1028  0.8731337653  302232   195981436499
1030  0.8443177018  214240    67697842111
1032  0.7919147337  123840     2340188621
1034  0.8470522110  214038    15092955791
1036  0.7825387960  167832     4749806249
1038  0.9575655965   83040        7777997
1040  0.8744748768  237120   347231600003
1042  0.8213473341  189644     1416993209
1044  0.7691513477  184788   410234894429
1046  0.8218743660  209200     3891938893
1048  0.8601385196  210648     2659949681
1050  0.7607034722  127050   286198762259
1052  0.7923620723  250376    46217768657
1054  0.8368529001  154938      338215609
1056  0.7644151486   89760      208497077
1058  0.8307721283  314226   747797555503
1060  0.7824557394  155820     3177411277
1062  0.7977441927  111510      505733909
1064  0.8564546152  156408      849704521
1066  0.7982755475  266500   284078285317
1068  0.8478768334   97188       68618423
1070  0.8264808233  265360   893218919371
1072  0.7754552986  273360   166587461267
1074  0.8686307359  110622      163626431
1076  0.7670245009  111904       14512039
1078  0.8511140984  113190       53349139
1080  0.8799842835   59400        4395199
1082  0.7680217132   96298        4050703
1084  0.8055816331  275336    84347645843
1086  0.8099434951  141180     3600296621
1088  0.9215699569  280704    39153022523
1090  0.7626480453  235440   407085806213
1092  0.8554992672   53508        2459029
1094  0.8095511766   65640         130411
1096  0.8213283778  289344   112671986677
1098  0.7816667884  200934   402811030067
1100  0.8339897725  231000   268074297247
1102  0.7387317926   76038        1532449
1104  0.7794659089  172224    75999313087
1106  0.8205856862  263228   234493195931
1108  0.8310993353  152904       84691319
1110  0.8598529624   89910      188373931
1112  0.7361306416  275776   206055104221
1114  0.7808359165  314148   481344775321
1116  0.8217937622  123876      770418163
1118  0.8601075905  216892     5180204077
1120  0.8854848018  248640   554542566943
1122  0.8264648520  124542     2657104391
1124  0.7998804113  171972      323087201
1126  0.8239936780  248846    11679983813
1128  0.8415828599  172584    17868227233
1130  0.7767269864  265550   993848893859
1132  0.8593262063  261492    12239261357
1134  0.9074951221  136080     2202840361
1136  0.9282887980  197664      293985487
1138  0.7790190677  334572   875195588849
1140  0.8076628284  111720     3294785161
1142  0.8700860381  238678     3367566031
1144  0.8223236332  260832   145906334257
1146  0.8317407053  113454      169035079
1148  0.8428018553  268632   155339123747
1150  0.8666095971  158700      724310183
1152  0.8352721397  175104    14039343203
1154  0.8594648293  153482       44201357
1156  0.7948368197  194208     1599584023
1158  0.8443111047   81060        7282003
1160  0.7892622029  214600    50021176927
1162  0.8204889884  270746   176705807177
1164  0.8102121131  182748    33540401473
1166  0.7784678789  257686    90657446557
1168  0.9572586699  153008       17010893
1170  0.7729929107   87750      419009483
1172  0.8229533295  298860    67591400683
1174  0.8060000295  190188      518421439
1176  0.8276281207  151704    13921176817
1178  0.7860532263  266228    75244938953
1180  0.7739208075  177000     4384360093
1182  0.7603415472  213942   432013072727
1184  0.8257881683  355200   737796275731
1186  0.7787172151  348684   879010204327
1188  0.8341177364  218592   521845216861
1190  0.7673368007  197540   175726677683
1192  0.8066264649  241976     5973880721
1194  0.8307393169  239994   537249220913
1196  0.8485558966  307372   237249620227
1198  0.8666707618  341430   140276755583
1200  0.8052107557  180000   301057281797
1202  0.7892545849  168280      153591049
1204  0.8024916553  198660     4217467523
1206  0.8113571022  170046     9797297701
1208  0.7764456913  269384    27754075967
1210  0.9195212184  151250      249315263
1212  0.8975392861   99384       16719533
1214  0.7872673892  335064   323108488037
1216  0.8269032484  272384    24305967857
1218  0.7633464614   71862       18526819
1220  0.7934630527  289140   925016379257
1222  0.8688803227  125866       10723477
1224  0.7931226203  127296      756415411
1226  0.7847327632  308952   103566586087
1228  0.9628472078  335244    22846348457
1230  0.8299957132  177120   164116573889
1232  0.7779899254  271040   501421393397
1234  0.8441010404  366498   338910798503
1236  0.9937793256  205176     5881514813
1238  0.8520820733  371400   341777579137
1240  0.8720733044  235600    20102921983
1242  0.9031175804  154008     1028600711
1244  0.8118095107  286120    22628017129
1246  0.7485481394  291564   624768581183
1248  0.8071402367  139776     1669994693
1250  0.9502378326  341250   435614000071
1252  0.7613410810  338040   384364562641
1254  0.8150021869  141702     3501299699
1256  0.8024067554  194680      365889319
1258  0.8045195501  218892     2746812779
1260  0.7783249914  134820    44756929403
1262  0.8253357424  157750       36532879
1264  0.8590688042  323584    46792093519
1266  0.8564775124  255732   379854613219
1268  0.8454746121  374060   309520787333
1270  0.8519223309  179070      739628081
1272  0.8404441177   86496        6689171
1274  0.7992530262  191100     2878941881
1276  0.7923741517  165880      249271471
1278  0.7470337014  217260   268066401913
1280  0.8015501664  291840   381307152827
1282  0.9026075528  330756    24659478631
1284  0.8179783108  174624     5559043583
1286  0.8626594506  236624      947968607
1288  0.8489703203  224112     5137486511
1290  0.7714562035  129000     4880106733
1292  0.7523462959  248064    24588119407
1294  0.8163890225  252330     3158891201
1296  0.8062660328  255312   572989131751
1298  0.7851752694  269984    37532187617
1300  0.8357809834  163800      596254669
1302  0.8278220097  203112   217717305569
1304  0.8780785965  117360        1609301
1306  0.7958292512  109704        1954877
1308  0.7705713692  217128   123478714061
1310  0.8005297721  170300      608216603
1312  0.7744069145  350304   351575334463
1314  0.7742978146  169506     5976303257
1316  0.8166795488  169764      267593939
1318  0.8343822169  208244      286965257
1320  0.7590711185  174240   428221441721
1322  0.8464749559  349008    71585765231
1324  0.8390435434  346888    74067423193
1326  0.7916075766  186966    58982927177
1328  0.7577211522  191232      329721311
1330  0.8365034558  143640      455443939
1332  0.7975648183  107892       48329459
1334  0.7964183670  302818    61633524781
1336  0.7992252582   89512         347359
1338  0.8258399582  135138      217363889
1340  0.8141227857  257280    42161008003
1342  0.7585621995  318054   302392716707
1344  0.8398689067  153216     2923780117
1346  0.7995989385  363420   197026432019
1348  0.8273846427  274992     4553982179
1350  0.7663641718  157950    24627840563
1352  0.8388127236  177112       97285039
1354  0.7998699715  284340     9101017421
1356  0.7947842030  166788     2508621751
1358  0.8774473024   66542          29669
1360  0.7687850787  171360     1152037177
1362  0.9254772153  207024     4586023759
1364  0.8445753475  237336     2504579141
1366  0.8085751065  413898   790909681031
1368  0.8042780008  248976   422349782843
1370  0.8211974417  300030   179864350037
1372  0.8426189479  124852        7711309
1374  0.7572586181  211596    56314236577
1376  0.8019054258  134848        7279231
1378  0.7811528653  227370     2397143887
1380  0.8534949799  187680    71579803181
1382  0.7949812035  154784       19583999
1384  0.7852662393  348768   108250429919
1386  0.7981000332   81774       21138983
1388  0.8304571419  366432    92582999071
1390  0.8176166213  262710    30060207601
1392  0.8345189990  180960     3586819427
1394  0.8901170706  426564   765606614939
1396  0.8703208693  346208    24135239603
1398  0.7936933989   83880        3499787
1400  0.8699736250  292600   313348432927
1402  0.7811078086  315450    27005623969
1404  0.7813071923  153036     1768265071
1406  0.7901574083  233396     1871670557
1408  0.8117808394  291456    19335103691
1410  0.8344413174  227010   643035696131
1412  0.8908828867  353000    20103009533
1414  0.8459935826  229068     1681944101
1416  0.7451507667  220896    94916206837
1418  0.7922573631  353082    78728030789
1420  0.7726141694  217260     5393984549
1422  0.7606996032  243162   223963253197
1424  0.8034136875  431472   988830904829
1426  0.7948264182  337962   105501996029
1428  0.7682037285  219912   720813177757
1430  0.8059057384  291720   843860733403
1432  0.8337565586  254896      998013763
1434  0.8224598828  289668   650680548121
1436  0.8669888432  359000    27798939227
1438  0.8191710469  383946   124763051197
1440  0.8397015903  231840   441867551599
1442  0.8105878067  147084       29920619
1444  0.8352306880  245480     1005429959
1446  0.8621117359  231360    18575687159
1448  0.7618131108  396752   478942837229
1450  0.8012145259  330600   614805510191
1452  0.8099784741  233772   132704330327
1454  0.8248157494  408574   220888711753
1456  0.7717799496  327600   615996218083
1458  0.8865366006  310554   456744825703
1460  0.7908192190  277400    52162033421
1462  0.7870688507  321640    51253409419
1464  0.9384838685  231312     6937695217
1466  0.7707432510  260948     2187935759
1468  0.9123662314  274516      637948453
1470  0.7674763769  113190     1255464179
1472  0.9491503556  110400         271829
1474  0.9472331671  243210      367827907
1476  0.7881256860  160884      903844567
1478  0.7744146696  297078     7971973831
1480  0.8737798400  281200    18428252767
1482  0.9405078032  125970       44241569
1484  0.7758347528  178080      213334811
1486  0.9056831879  338808     5642416463
1488  0.8424399808  116064       22672409
1490  0.8059188055  338230   365893799413
1492  0.8584211730  474456   687238610533
1494  0.8889146296  165834      286151689
1496  0.8058633218  372504   469423511377
1498  0.8137789443  167776       65793991
1500  0.7927895694  241500   965797824143
1502  0.9961616621  489652   131264869717
1504  0.8031530823  380512   104399857741
1506  0.7914123621  239454    48237455489
1508  0.8026243598  313664    29724171107
1510  0.8195839147  277840    21041457247
1512  0.8901068072  136080      147752147
1514  0.8358192940  410294   116577153899
1516  0.8216384656  122796        1154401
1518  0.8175681303  242880   192640527727
1520  0.9041079974  101840        1081919
1522  0.8111169528  321142     8175394519
1524  0.7905343730  193548     3732368281
1526  0.8302854915  260946     3667616923
1528  0.8750757684  406448    54495373589
1530  0.8072636196  107100      118049251
1532  0.8541578511  228268      132366211
1534  0.7887322796  329810    44159526041
1536  0.8294899278  302592   391179941417
1538  0.8900936125  482932   349356891361
1540  0.8038640651  147840      316785277
1542  0.8214834996  262140    69530754089
1544  0.8764917307  328872     3975074731
1546  0.7903584021  103582         351991
1548  0.8383000265  275544   123267268679
1550  0.8413448913  255750     5960290789
1552  0.8114620618  356960    24769297559
1554  0.7800808591  186480    16450544519
1556  0.8568898932  171160        9112993
1558  0.8218188396  433124   562280452403
1560  0.9157356241  209040    38800435783
1562  0.7846883323  285846     8076556171
1564  0.7980940759  142324        8025379
1566  0.8167158909  239598    30055080409
1568  0.7662213251  370048   439180274941
1570  0.7746854062  348540   458704065011
1572  0.8184291024  248376    31025735201
1574  0.9112372759  443868    64781923543
1576  0.7817187781  463344   873638867083
1578  0.7501763097  249324    86601064799
1580  0.7839677575  336540   246027641549
1582  0.7730511838  317982    55559709001
1584  0.7755140904  182160     4047135847
1586  0.7612707125  326716    40097484313
1588  0.9103561109  435112    46646711977
1590  0.7589757414  222600   340026160073
1592  0.8077489694  302480     2776054133
1594  0.7767897475  412846   166722435487
1596  0.7754022024  242592   486832610599
1598  0.8150241334  239700      480033497
1600  0.8357905158  385600   457527909493
1602  0.8328473544  299574   216468938123
1604  0.8492583744  384960    21765583711
1606  0.8567775969  367774    40189568197
1608  0.8337536939  242808    15831375793
1610  0.7575073997  204470     6598899149
1612  0.7583742677  201500      220008827
1614  0.8291248670  227574     6725374343
1616  0.7840603817  463792   644696035957
1618  0.8117011999  218430       84053447
1620  0.7870627730  115020       97103599
1622  0.7751631436  382792    52875290749
1624  0.7802624067  391384   733429437133
1626  0.8167486714  292680   154053460247
1628  0.9446193129  315832     2283953137
1630  0.8194852195  396090   726191365061
1632  0.7550492192  213792    16333925009
1634  0.7538921106  303924    10686653603
1636  0.8316850879  397548    32452593779
1638  0.7900243382  185094    12998320499
1640  0.8098864352  218120      810783059
1642  0.8434343319  344820     4979733131
1644  0.8114258736  325512   621631571797
1646  0.8438360800  355536     6798510007
1648  0.8263286083  138432        1531627
1650  0.7989483523  158400     4664280787
1652  0.9250945548  454300   343615288279
1654  0.8615092622  119088         296071
1656  0.8304681782  273240    69376776431
1658  0.7703138283  464240   520875254171
1660  0.7810367456  111220        2392849
1662  0.8077601354  299160   177539425109
1664  0.7641347548  389376   153720920827
1666  0.7930800970  138278        9758249
1668  0.8305064229  286896    73180041931
1670  0.8037069898  145290       14505989
1672  0.7774124481  197296      142244881
1674  0.7947103457  323082   824600529751
1676  0.7824985936  489392   756257790839
1678  0.8134032000  290294      916951853
1680  0.8032316703  226800   597856288817
1682  0.7890299302  417136   120640880671
1684  0.8306205080  368796     9654196753
1686  0.8051637821  338886   805841782637
1688  0.8921039317  140104         727459
1690  0.7709285665  348140   482172383669
1692  0.8391521121  270720    31561476641
1694  0.7782847752  211750      656975563
1696  0.8069216888  325632     3669800957
1698  0.8167651776  249606    12863275951
1700  0.7821441073  353600   348891508463
1702  0.8054476993  418692   133748444587
1704  0.8140891751  102240        3087559
1706  0.8075483346  506682   610237668457
1708  0.8131242893  428708   565239599681
1710  0.7634204137  227430   253930232167
1712  0.8691123645  352672     3163566949
1714  0.8095219202  351370     6017940139
1716  0.8835409129  281424   153972987853
1718  0.8739398975  455270    50262417851
1720  0.7855599472  216720      630058997
1722  0.7641267074  268632   566632213241
1724  0.8364811742  415484    27365092943
1726  0.8702593613  491910   132170458579
1728  0.8179724409  293760    69865330459
1730  0.8260436073  238740      796386601
1732  0.7819358459  327348     3628398619
1734  0.7753069499  192474     1894619563
1736  0.8016654968  421848   550614481399
1738  0.8457275455  295460     1552723541
1740  0.7919091535  269700   942418210157
1742  0.7605712758  343174    23224145863
1744  0.8206799011  301712      908630861
1746  0.7668895117  336978   989005036879
1748  0.8489170114  215004       58165519
1750  0.8036402877  329000   220927232189
1752  0.8616990408  313608    82534284533
1754  0.8473411261  152598        1533881
1756  0.7706128013  393344    30433528379
1758  0.7659440201  288312   106124242957
1760  0.8157338655  170720       71193821
1762  0.9324450426  155056         778237
1764  0.8662757547  123480       19997011
1766  0.8975798223  392052     4619500177
1768  0.7929301973  141440        4014743
1770  0.8060107459   46020          19681
1772  0.7942291618  398700    22347576533
1774  0.8826296816  523330   171717935677
1776  0.7805723788  248640    16329074077
1778  0.8363428692  147574        4166893
1780  0.7650138123  309720    25985058947
1782  0.8357838056  326106   472067425033
1784  0.7468729741  374640    20986352311
1786  0.8186613485  251826      234606587
1788  0.7930963908  185952      439282859
1790  0.7693801021  309670    21173197777
1792  0.8161538174  360192    25751872571
1794  0.8204215358  175812      561253949
1796  0.9181328361  290952      146765011
1798  0.8196685998  384772    18475888159
1800  0.8037826031  252000   125682673591
1802  0.8243736668  365806    10706324677
1804  0.8112883773  200244       42297383
1806  0.7695197161  270900   300560704487
1808  0.8071400369  316400     1212895577
1810  0.8243813029  266070     1566501623
1812  0.7996329080  246432     6960357979
1814  0.8102967233  186842        8294009
1816  0.8254743325  526640   344609374943
1818  0.8205975986  301788    56510444411
1820  0.8336934480  182000      284817059
1822  0.8836892131  606726   849507698503
1824  0.7845596590  302784   174404721223
1826  0.8512158126  219120       49305547
1828  0.7604210417  380224    14757755347
1830  0.8121256931  186660     3186734437
1832  0.8642064575  309608      404865341
1834  0.8268278495  308112     3108322541
1836  0.8752751436  358020   374304548171
1838  0.7795998180  435606    51826125163
1840  0.8491828568  386400   109948598423
1842  0.8037202603  167622      103867579
1844  0.8422012103  566108   548310882851
1846  0.8135778231  426426    70538949601
1848  0.7738559721  166320     1547922247
1850  0.8302054328  303400     6086292517
1852  0.8449287789  314840      526114601
1854  0.8109908179  198378      481252351
1856  0.7827345123  504832   448634754871
1858  0.8013384211  505376   209723416667
1860  0.7828801817  206460    15124158563
1862  0.8057309920  368676    48351869201
1864  0.7783584477  492096   216582156223
1866  0.8583789450  121290        3479017
1868  0.7891773366  467000    87756081911
1870  0.8528609009  250580     2019315719
1872  0.7783608093  308880   250773184159
1874  0.7808045026  376674     7236843893
1876  0.9080331830  388332    12355917811
1878  0.8310995775  375600   487167968143
1880  0.9133843806  101520         115733
1882  0.7587750467  333114     2429422103
1884  0.7546195033  341004   486548431247
1886  0.8490392178  428122    24883483561
1888  0.8099599707  135936         556601
1890  0.7522935441  109620       94548211
1892  0.8139760522  391644    24776396627
1894  0.9023584626  253796       30538631
1896  0.7927459139  318528   104817963919
1898  0.7747108816  364416    13596122233
1900  0.7910605148  121600        2095099
1902  0.8264780717  351870   187070600377
1904  0.8230051183  331296     8766482833
1906  0.8298397339  486030    59168915753
1908  0.7651017474  362520   927600976259
1910  0.8015908325  236840      365403209
1912  0.7894504811  430200    24577842413
1914  0.8006393792  294756   136562225687
1916  0.8752066970  488580    31235004469
1918  0.8673173967  184128        9932411
1920  0.8148307257  289920   280970804167
1922  0.8292670435  493954    97958090899
1924  0.8166896263  307840     1177653787
1926  0.7756757343  177192      169928047
1928  0.8575486386  366320     1448880317
1930  0.8515978608  318450     3829010369
1932  0.8121379332  278208   115369438139
1934  0.8067202609  529916   211342935941
1936  0.8144614633  174240        5733881
1938  0.7571646653  155040      154161961
1940  0.8063007227  168780       14620343
1942  0.8098957594  547644   292790220277
1944  0.7924631949  176904      114840017
1946  0.8224680982  515690   893289156899
1948  0.9131916474  516220    29743421713
1950  0.8280858762  193050     3724402597
1952  0.8411324666  464576    26124348431
1954  0.8045655396  361490     2079759221
1956  0.8360620907  338388    71429569121
1958  0.9042408606  391600     4308308863
1960  0.8199068785  388080   335725437139
1962  0.8578620403  392400   345609175889
1964  0.8345424979  595092   518696590459
1966  0.8878075384  440384     5764421087
1968  0.8242033374  202704      326011687
1970  0.8599057873  128050         838813
1972  0.9263154811  605404   536212777627
1974  0.8058616819  173712      381960377
1976  0.8133574376  468312   162651150481
1978  0.7688230914  195822       16041257
1980  0.8040018986  138600      169811309
1982  0.7799955167  142704         658783
1984  0.8626775173  432512     8410429151
1986  0.8786959000  162852       18787777
1988  0.8778215869  447300    49713998333
1990  0.8857322728  222880       54878167
1992  0.8009272405  225096      975153437
1994  0.8396915640  502488    44186280899
1996  0.7769341985  499000   106759181827
1998  0.7808272591  291708    26780243779
2000  0.8303456888  450000   201178467727
2002  0.8409817386   90090         108247
2004  0.8162851392  390780   458416204973
2006  0.8133753129  575722   986730463219
2008  0.8486375398  301200      151695521
2010  0.8342503869  190950     1102112779
2012  0.7734880161  150900         981241
2014  0.7671073980  410856    24475888897
2016  0.8022571460  100800        2494931
2018  0.8494843501  571094   164359880327
2020  0.8230863367  185840       19584923
2022  0.8223481384  167826       36845153
2024  0.8309974663  313720      988855327
2026  0.8499433341  324160      269446063
2028  0.8022611442  328536   133553332753
2030  0.8242912742  182700       76961683
2032  0.7532147258  426720    19766689993
2034  0.7633475922  223740     1174845277
2036  0.8650469107  669844   976322565739
2038  0.8052727506  591020   458260673729
2040  0.8673139995  161160      187558487
2042  0.7713295232  512542   121570066711
2044  0.8180119882  531440   810931356317
2046  0.8406930268  126852        7584587
2048  0.8287089447  399360     2638382221
2050  0.8422145540  297250     1323968101
2052  0.7635963015  371412   791621591347
2054  0.8056918341  264966      137967671
2056  0.9004069331  370080      501823219
2058  0.7736203277  294294   111286076497
2060  0.8464353018  339900     4307409313
2062  0.7738079266  216510       14169509
2064  0.7671997593  179568      127208503
2066  0.7957309556  402870     4161647461
2068  0.7962319592  475640   116542754561
2070  0.8054098595  254610    42330464461
2072  0.7572386641  198912       37172491
2074  0.8605307290  234362       20415251
2076  0.7328372308  323856   101585037611
2078  0.8497631914  320012      186824381
2080  0.7690591176  386880   130335577469
2082  0.8642095759   97854         261353
2084  0.7672957897  462648    28648417081
2086  0.7578902693  496468   624606681343
2088  0.7920905581  377928   373441418069
2090  0.7941092867  413820   482822510809
2092  0.8587631447  238488       11873581
2094  0.8158097160  226152      464645191
2096  0.8278178826  358416      726129623
2098  0.8226243099  646184   776204672279
2100  0.7449312847  186900     8493730699
2102  0.8744268703  529704    27004622947
2104  0.8550402355  315600      141068119
2106  0.9474544600  284310     2216585531
2108  0.7511290690  510136   355953567793
2110  0.8009896331  485300   460999262291
2112  0.7393471766  139392       28304827
2114  0.7898848115  348810     4168465507
2116  0.8649817218  634800   495720674831
2118  0.9051849321  239334      260676187
2120  0.8351590397  288320      702105401
2122  0.7688711986  475328    30775211123
2124  0.9388700643  494892   894886546531
2126  0.8456247514  669690   723771797797
2128  0.7990810652  468160   203764431313
2130  0.8139219860  296070   117134810327
2132  0.8072488682  319800      663955883
2134  0.7711317831  486552   136126359241
2136  0.8628783707  350304    26857654469
2138  0.8657888815  634986   240353464553
2140  0.8960751240  374500     4378874677
2142  0.7993218844  119952       10112197
2144  0.7945590063  383776     1941073177
2146  0.7891104983  564398   370272189899
2148  0.7732375218  356568   112839406373
2150  0.8331469874  283800      556400347
2152  0.7968894047  561672   136772783111
2154  0.8311032470  174474       27143603
2156  0.7803814971  409640    71872165709
2158  0.8375276941  308594      253146317
2160  0.9376729050  380160   332714549693
2162  0.7908718147  473478    36566435363
2164  0.8154457889  393848     1527717791
2166  0.7984010056  379050   276560036659
2168  0.7659054961  513816    66683488213
2170  0.9431982536  288610      897296623
2172  0.7720492907  373584   181441374769
2174  0.8078314291  221748        7806221
2176  0.8449114551  361216      747554851
2178  0.8055899389  280962     9625032539
2180  0.8018843811  270320      378596093
2182  0.9210391264  473494     2701520953
2184  0.7654168402  100464        3495823
2186  0.8016100263  413154     2723037113
2188  0.8976738587  676092   254424267029
2190  0.8363533681  208050     1059796799
2192  0.8351214808  624720   244199115887
2194  0.8684701090  636260   169209614501
2196  0.7772574036  223992      488025271
2198  0.7891215994  419818    22589954983
2200  0.8883427140  228800       61787291
2202  0.7887802821  118908        1588801
2204  0.8458308451  372476     1194713543
2206  0.7848417164  337518      379223861
2208  0.8199545230  295872     6796402447
2210  0.9119845144  335920     3243341317
2212  0.8586024767  387100     3399889981
2214  0.8471435342  414018   206470904039
2216  0.8021249047  285864       63239083
2218  0.8778924796  678708   296412366823
2220  0.7880128324  137640       36399353
2222  0.7649112784  226644       29674187
2224  0.8295824011  420336     2013164977
2226  0.8709747186  333900    58154921369
2228  0.8376555482  434460     2394970429
2230  0.8243787540  294360      511045949
2232  0.8107895334  214272      208930949
2234  0.8638791103  355206      216493477
2236  0.8503672287  221364        9310507
2238  0.8901411615  467742   348134738267
2240  0.8055637999  356160    26314798501
2242  0.8226424209  363204      852887743
2244  0.8681184286  195228      138150269
2246  0.8474866418  572730    45551492071
2248  0.8250100800  512544    16922727467
2250  0.8254644474  265500    11355705887
2252  0.8218322114  682356   636232475033
2254  0.8542551982  513912   120644298881
2256  0.8629248633  196272       42919049
2258  0.7891834514  426762     3227872051
2260  0.7749354667  187580       13560257
2262  0.8158831853  291798    10448276911
2264  0.8420737848  713160   794388396031
2266  0.8338951629  317240      243635459
2268  0.8481414977  233604      898653529
2270  0.8862233708  497130    65827577419
2272  0.7644786846  483936    21130374217
2274  0.8764404650  450252   209476646777
2276  0.7764284024  546240    64234545953
2278  0.7532676674  435098    14358928049
2280  0.8268772522  326040   230604681031
2282  0.7882391727  561372   569736287669
2284  0.8117097930  678348   573664146221
2286  0.8637388287  137160        1831987
2288  0.7869488679  526240   289856428051
2290  0.7920970940  178620        6568031
2292  0.7649375313  339216    30949412261
2294  0.8325578826  346394      333953699
2296  0.7792436901  523488   308002613761
2298  0.7541889590  358488    68022309503
2300  0.8125797241  522100   543376141813
2302  0.8141515820  347602      233021161
2304  0.8594340588  481536   537492065717
2306  0.9154130802  219070        1598617
2308  0.7894156522  660088   501816932311
2310  0.7799182950   78540        1873513
2312  0.8674247228  462400     4102401619
2314  0.7925051756  520650    67980657709
2316  0.8592528052  252444      311826077
2318  0.8561397222  222528        5240101
2320  0.8718135463  584640   760793625643
2322  0.8588823907  390096    44148299231
2324  0.7732456619  525224   257267005013
2326  0.8557835135  397746      484497023
2328  0.8945424266  311952     1795974079
2330  0.8328593105  370470     3222623119
2332  0.7693951284  345136     1045858357
2334  0.8484177520  163380        6778033
2336  0.8112627080  546624    31856145323
2338  0.8585159682  586838   238401125849
2340  0.7546329465  262080    46136691787
2342  0.9229298450  733046   206761566857
2344  0.8076481205  696168   628074675289
2346  0.7925852775  326094    31546997333
2348  0.8358341918  612828    72860992511
2350  0.8283901892  192700        7857313
2352  0.8449394678  359856    85762575343
2354  0.8123041008  211860        6279617
2356  0.9064519315  438216     1543003597
2358  0.7788593874  124974        1569307
2360  0.7757682740  500320   281201402173
2362  0.7291885369  621206   466877434043
2364  0.7783902085  144204        4598203
2366  0.8215129092  288652      259406821
2368  0.8829131011  748288   602114594209
2370  0.8865971719  177750       60713161
2372  0.8035193297  389008      604842781
2374  0.7667369906  678964   736261556533
2376  0.8810062237  299376     2721742963
2378  0.7927634714  670596   861622073677
2380  0.7745299000  299880     5638758737
2382  0.7680549495  200088       75057643
2384  0.8282466611  717584   559793447813
2386  0.8772966704  262460        7327763
2388  0.8058200406  355812    17966184359
2390  0.8975224664  255730       32354719
2392  0.8043241802  581256   229668981863
2394  0.8090253541  105336        1327111
2396  0.8580344286  618168    45611223223
2398  0.7865336675  316536      241507381
2400  0.7635251277  352800   467043338761
2402  0.9031048934  384320      150433103
2404  0.8137395535  497628     6367483051
2406  0.8520553527  120300         467867
2408  0.7678051922  553840   414680346433
2410  0.7780260570  400060    11248596199
2412  0.8405729453  313560     2662138627
2414  0.7711131520  557634   108509711657
2416  0.8299590654  645072   112907977309
2418  0.7618561842  372372   206729972041
2420  0.7905715096  326700     2577433259
2422  0.8737056997  636986   349313358767
2424  0.8463147292  509040   809631798277
2426  0.8648306484  788450   815028696011
2428  0.7900032871  463748     3612270863
2430  0.7915394356  247860     3522895501
2432  0.8680034376  437760     1221059317
2434  0.8000074355  705860   499446658943
2436  0.8087405849  158340       25720103
2438  0.8163448566  402270     1031162347
2440  0.8904128070  470920    15615750541
2442  0.8619274920  344322    16972376501
2444  0.7868834861  630552   501782372369
2446  0.7673643592  511214    13811727857
2448  0.7916674170  119952        1139227
2450  0.7976379815  502250   777219739931
2452  0.9585963388  210872         453137
2454  0.8572029328  171780        6223667
2456  0.8258166895  456816     1707851083
2458  0.8194532445  297418       28965733
2460  0.8244748324  383760   515369429777
2462  0.8511266276  679512   116020335329
2464  0.7706291229  544544   606227974559
2466  0.7963644070  424152   124573828051
2468  0.9329576496  244332        1903301
2470  0.7435891544  479180   725601206171
2472  0.8119016402  499344   837629197919
2474  0.8361829894  482430     2414960227
2476  0.7960159596  661092   180959311921
2478  0.8569843105  344442    27315473041
2480  0.8194362764  540640   242838561517
2482  0.8501855564  402084      629876623
2484  0.7552473256  375084    75041495759
2486  0.8124169631  504658    16898103349
2488  0.7859003369  686688   337606158101
2490  0.8037901955  313740    39233353787
2492  0.8083494058  221788        9787039
2494  0.7827044010  177074         878873
2496  0.8199349432  476736   890407957763
2498  0.8300985187  262290        7873469
2500  0.8459473672  372500     1297710119
2502  0.8787444409  330264     1789037759
2504  0.8734452768  280448        8967173
2506  0.8044716080  473634    15732838523
2508  0.8000543786  378708   136621802293
2510  0.8296760210  542160   126417684163
2512  0.8467662766  195936         623671
2514  0.8365770068  372072    10401056257
2516  0.8076722078  626484   185892132809
2518  0.8782289295  458276      699575441
2520  0.7815450228  115920        9196807
2522  0.8104566307  514488    15661557383
2524  0.8313015963  373552      158677777
2526  0.7801749658  255126      370356221
2528  0.7756992109  723008   739035352871
2530  0.7972433038  349140     4878244649
2532  0.7679961125  177240       15619469
2534  0.7845873694  572684   195163249889
2536  0.7832586885  705008   388369699811
2538  0.8136339962  246186      200232311
2540  0.8004875429  594360   612283207313
2542  0.8989147199  394010      199219799
2544  0.8400237991  172992        6629387
2546  0.8399063742  621224    68610331883
2548  0.7523453472  443352    31676007821
2550  0.8196549026  280500    11029796251
2552  0.7751988286  658416   911302288367
2554  0.7778223327  574650    28189790411
2556  0.7905006100  173808       10451179
2558  0.8567957666  828792   887593062737
2560  0.8212147618  529920    79821713953
2562  0.7586665234  335622    58222542601
2564  0.7928609611  597412    34435934821
2566  0.8424737721  713348   144959825909
2568  0.8061790647  210576       41679137
2570  0.9619459674  354660      173713313
2572  0.8130912819  733020   321913725169
2574  0.7915056411  375804   142064839619
2576  0.7905255410  602784   467861927717
2578  0.7887216191  742464   550708199563
2580  0.7743905635  291540    19029001837
2582  0.9437094381  818494   182400714409
2584  0.8274264593  552976    28863485671
2586  0.8373883588  426690    37263350507
2588  0.8145755184  768636   545439097163
2590  0.7694910475  427350   102509369951
2592  0.8487067279  427680    30786910439
2594  0.9041436410  365754       46717493
2596  0.8053648183  576312    61189450727
2598  0.8076647220  470238   187849378111
2600  0.8273546596  221000       17331641
2602  0.8401129167  572440     8765438179
2604  0.8326267909  221340      221053711
2606  0.8221688680  719256   180904315547
2608  0.7968833417  469440     1815973217
2610  0.7977052404  373230   288089409547
2612  0.7707861529  417920      716956337
2614  0.8594118059  784200   301693020571
2616  0.7315603326  164808       10134331
2618  0.8412065298  314160      367727071
2620  0.7613793196  589500   707529794791
2622  0.7390603437  401166   234187524581
2624  0.7732717061  663872   176800661201
2626  0.7653767382  603980   137080434437
2628  0.7765421620  420480    74507762587
2630  0.8408173934  649610   619119337283
2632  0.7923082847  626416   418876194211
2634  0.8451563971  521532   336262377679
2636  0.8607846111  229332        1281899
2638  0.8167139746  582998    12795204341
2640  0.8226472501  290400    15836332901
2642  0.7854687566  435930      803368823
2644  0.7685865001  727100   423129900653
2646  0.8781688819  412776    67465005107
2648  0.8641502338  701720    59115954797
2650  0.8209442976  445200     8263436131
2652  0.8158978442  434928   276568689209
2654  0.7989051547  398100      262029809
2656  0.7993877234  172640         200591
2658  0.8279609779  465150    88792250263
2660  0.8158176891  452200   100019816647
2662  0.8225958214  324764       69628499
2664  0.8279695897  535464   761878688143
2666  0.7746957069  610514    72657935507
2668  0.8726439435  664332    62481289817
2670  0.8646908085  416520   229185148609
2672  0.7877402928  790912   873917725651
2674  0.7922077633  574910    90681187253
2676  0.8134087029  503088   289469802851
2678  0.8078425394  297258       33589921
2680  0.8165051269  450240     8397761893
2682  0.7903008119  219924       48541973
2684  0.7815422369  523380    18175376237
2686  0.8114513610  539886    10655490721
2688  0.8109550571  325248     8405709199
2690  0.8155768850  169470         943429
mart_r is offline   Reply With Quote
Old 2020-06-03, 18:11   #18
mart_r
 
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you know...around...

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Just for fun, I let my program look for q up to 3*105 for a couple millions of p, and within one day, I found more than 50 new extraordinarily large gaps (larger than \varphi(q)*log²(p)). The largest of them has g/[\varphi(q)*log²(p+g)]~1.14086 (p=202,722,071 / q=60712). So there's a lot of unexplored territory.

I'll try to set a new record here in terms of CSG and probably post some results by Friday.

BTW, q<=1000 currently @ p=4.8*1012, q<=2690 @ p=1.8*1012, no major findings in the last few days. Progressing.
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Old 2020-06-07, 12:30   #19
mart_r
 
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you know...around...

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prob·a·bly adv. very likely; without much doubt (Webster's New World basic dictionary of American English)
If a number P between 0 and 1 should be assigned in this regard, how large would it be?

Anyway, here's some data for posterity:
Code:
                                                             gap/phi(q)/    CSG-method
       gap           p          p'    k         q        r      log²(p')    Sum Ri'(x)  who/year
  26026560   150211753   176238313  112    232380    94273  1.1658890306  1.1753290815  Raab 2020
   3906628   190071823   193978451  209     18692    11567  1.1480589845  1.1491888083  Kourbatov/Wolf 2017
  12749520   202722071   215471591  210     60712     4703  1.1408583553  1.1443595696  Raab 2020
  44221268    19019009    63240277  182    242974    67037  1.1281678511  1.1916358202  Raab 2020
  21106128  1560734261  1581840389  167    126384    18245  1.1170554360  1.1177296369  Raab 2020
   8083028   344107541   352190569  206     39238    29519  1.1134625422  1.1147048561  Kourbatov/Wolf 2017
  31135962   916198957   947334919  143    217734   192019  1.1049327614  1.1066623864  Raab 2020
  43706268   403761601   447467869  146    299358   227017  1.1039772763  1.1095079567  Raab 2020
  58244058   219789979   278034037  139    419022   222451  1.1031048845  1.1158890335  Raab 2020
   9403290  1015173661  1024576951  117     80370    20191  1.0992710599  1.0997196593  Raab 2020
  20655000     7827217    28482217   81    255000   177217  1.0953885874  1.1632317742  Raab 2020
  63203910    85252241   148456151  165    383054   214253  1.0875048872  1.1170637202  Raab 2020
  12312360    42545843    54858203  115    107064    41435  1.0871339798  1.1018732870  Raab 2020
  76697040   325087801   401784841  210    365224    38441  1.0870612491  1.0982670091  Raab 2020
  35920626   284354281   320274907  119    301854     7813  1.0860305010  1.0924116630  Raab 2020
  13720800     3216881    16937681  120    114340    15361  1.0829962394  1.1674502497  Raab 2020
  15670164    57747743    73417907  177     88532    24879  1.0792088227  1.0928849191  Raab 2020
    208650     3415781     3624431   65      3210      341  1.0786589153  1.0821910132  Kourbatov/Wolf 2017
  40233294   129394039   169627333  129    311886   273235  1.0778496711  1.0925310542  Raab 2020
  42576716    53707037    96283753  182    233938   135235  1.0771626660  1.1085952932  Raab 2020
  26994402    68872591    95866993  171    157862    44759  1.0760433707  1.0943950612  Raab 2020
  18491724   508984297   527476021  138    133998    59893  1.0741607074  1.0759988158  Raab 2020
   2157480    13074917    15232397   78     27660    19397  1.0716522452  1.0809485789  Kourbatov/Wolf 2019
  24502010   675559229   700061239  205    119522    20885  1.0710260557  1.0728404154  Raab 2020
   3415794   376981823   380397617  201     16994     3921  1.0703375544  1.0707668266  Kourbatov/Wolf 2017
  72750990   279155309   351906299  195    373082    89973  1.0701202187  1.0822289562  Raab 2020
  10876660    18970891    29847551  155     70172    24451  1.0698062013  1.0960456465  Raab 2020
  48318616   457558447   505877063  212    227918   127021  1.0692343217  1.0744489116  Raab 2020
   1530912   728869417   730400329  222      6896     3593  1.0684247390  1.0684935933  Kourbatov/Wolf 2017
  11563370   381674801   393238171  131     88270    83591  1.0679043611  1.0694410998  Raab 2020
  67002754   155635027   222637781  169    396466   220355  1.0673928908  1.0862011035  Raab 2020
  34710336   646336727   681047063  216    160696    17415  1.0671818425  1.0698537690  Raab 2020
  60029536   236847133   296876669  203    295712   277533  1.0668680315  1.0787516718  Raab 2020
  31111720   338212681   369324401  166    187420   107001  1.0665081217  1.0711276926  Raab 2020
  45480858    37855579    83336437  177    256954    83341  1.0642247130  1.1053573836  Raab 2020
  52973904   272681197   325655101  136    389514    21397  1.0619276093  1.0712027205  Raab 2020
  21486816    58954163    80440979  117    183648     3155  1.0598554173  1.0769849413  Raab 2020
   1896608      164663     2061271  112     16934    12257  1.0598397341  1.1852239238  Kourbatov/Wolf 2017
  55129728   131328623   186458351  192    287134   108385  1.0588409893  1.0773034386  Raab 2020
  30580280    31606847    62187127  170    179884   127147  1.0557711073  1.0918855069  Raab 2020
  10355604   856609109   866964713  183     56588    36553  1.0545686348  1.0551433620  Raab 2020
   5403024   262789987   268193011  132     40932     6547  1.0541831039  1.0552109864  Raab 2020
  20332800    88927171   109259971   96    211800   182971  1.0537979234  1.0649986104  Raab 2020
 132625590     2839657   135465247  115   1153266   533125  1.0536024200  1.1675846988  Raab 2020
  41112864  1720833797  1761946661  234    175696    67173  1.0533569871  1.0544909778  Raab 2020
  10723372  1626559621  1637282993  202     53086     4581  1.0503858509  1.0506827685  Raab 2020
  14065200   965324803   979390003  180     78140    61383  1.0502207536  1.0509147496  Raab 2020
  31303064   734306093   765609157  194    161356   136293  1.0501770849  1.0522589060  Raab 2020
  28427040   565631527   594058567  171    166240    83047  1.0484424049  1.0509123457  Raab 2020
   7230930   130172279   137403209  147     49190    15539  1.0468373915  1.0497240560  Kourbatov/Wolf 2019
  61008404   543640997   604649401  214    285086   267081  1.0468336353  1.0521974766  Raab 2020
  17611524    87652883   105264407  153    115108    55695  1.0465179793  1.0564849581  Raab 2020
   9436848     8241139    17677987  141     66928     8995  1.0463975066  1.0892125979  Raab 2020
   4575906    20250677    24826583  101     45306    44201  1.0463153374  1.0581819483  Kourbatov/Wolf 2019
   7144760    30340823    37485583  119     60040    20623  1.0457650931  1.0578359289  Raab 2020
  39775736   275592497   315368233  182    218548     3469  1.0457625466  1.0527464522  Raab 2020
  16545222   197273641   213818863  123    134514    76117  1.0445103314  1.0487427115  Raab 2020
  34294350    94055281   128349631   97    353550    10981  1.0439655485  1.0604085140  Raab 2020
  85968122   206916719   292884841  181    474962   308249  1.0437080792  1.0613402928  Raab 2020
  16771540    57106657    73878197  137    122420    58937  1.0435528764  1.0576844880  Raab 2020
   2972664     5323187     8295851   82     36252    30395  1.0427690852  1.0695379542  Raab 2020
  18982866    16732321    35715187  129    147154   103919  1.0427244923  1.0834115109  Raab 2020
   5609136    34016537    39625673  104     53934    38117  1.0412524005  1.0499075334  Kourbatov/Wolf 2019
 260917668    36356059   297273727  198   1317766   776377  1.0403369145  1.1212483771  Raab 2020
  47687280    54427211   102114491  115    414672   105179  1.0403195742  1.0726213426  Raab 2020
1153282126    40569031  1193851157  227   5080538  5005265  1.0393091300  1.1352839382  Raab 2020
  22513392   345811177   368324569  198    113704    37313  1.0392757594  1.0425001861  Raab 2020
  29611680   118797403   148409083  147    201440   149243  1.0388950704  1.0506756093  Raab 2020
  26092110    69321059    95413169  165    158134    58367  1.0388234360  1.0559600795  Raab 2020
   2413620      355417     2769037   53     45540    36637  1.0386945028  1.1428002353  Raab 2019
   8160768   230301523   238462291  144     56672    43187  1.0384490461  1.0402329592  Raab 2020
  30255160  1085694133  1115949293  166    182260   153573  1.0373558283  1.0386795991  Raab 2020
   3422630      735473     4158103  115     29762    21185  1.0368176014  1.1281161479  Kourbatov/Wolf 2017
  32799228   582134099   614933327  121    271068   151103  1.0363422342  1.0390636915  Raab 2020
  24892056   204946981   229839037  189    131704    15557  1.0363200824  1.0422994383  Raab 2020
   6415812  1693755359  1700171171  234     27418     8409  1.0360874064  1.0362451823  Raab 2020
  11456256  1067601151  1079057407  192     59668    21295  1.0360534914  1.0365493807  Raab 2020
  32356272     2058179    34414451  104    311118   191471  1.0360111463  1.1431414554  Raab 2020
  40713186    90187127   130900313  177    230018    20071  1.0358686339  1.0553593797  Raab 2020
  27299290  1237841221  1265140511  179    152510    70061  1.0358141038  1.0368533648  Raab 2020
  17399370   440876999   458276369  159    109430    92959  1.0356890307  1.0376268994  Raab 2020
  45020928   327791159   372812087  192    234484   217011  1.0356338254  1.0421886699  Raab 2020
  25581952    76769131   102351083  176    145352    23275  1.0348088479  1.0501799186  Raab 2020
  34372654    85955479   120328133  179    192026   119857  1.0341748708  1.0518985513  Raab 2020
    984170     5357381     6341551  115      8558       73  1.0339720553  1.0443452341  Kourbatov/Wolf 2017
  40743736   447004813   487748549  188    216722   124049  1.0335560254  1.0379415282  Raab 2020
  45684090    94980541   140664631   97    470970   315571  1.0335532853  1.0538225485  Raab 2020
   2266530   198565889   200832419  129     17570     7319  1.0335372951  1.0340700214  Kourbatov/Wolf 2017
   7125388  5088100651  5095226039  251     28388     5859  1.0335068728  1.0335565879  Raab 2020
  19609800   508010863   527620663   92    213150    74413  1.0334994824  1.0353716750  Raab 2020
  53269880    58846181   112116061  142    375140   324341  1.0333898957  1.0660891427  Raab 2020
  25371000  1138678631  1164049631  180    140950    84531  1.0330147550  1.0340650943  Raab 2020
  42800280    98683987   141484267   97    441240   287467  1.0329970144  1.0516497002  Raab 2020
  30754304  1077939353  1108693657  224    137296    28457  1.0329949635  1.0343472582  Raab 2020
  46071424  1065488737  1111560161  224    205676    87057  1.0326385929  1.0346848669  Raab 2020
  63992864     8219327    72212191  169    378656   267551  1.0323583994  1.1211359112  Raab 2020
  41919540   260566829   302486369  130    322458    20765  1.0316370313  1.0392505301  Raab 2020
    316790      726611     1043401   79      4010      801  1.0309808771  1.0553139996  Kourbatov/Wolf 2017
  14359440     8356739    22716179   76    188940    43379  1.0302944159  1.0825626844  Raab 2019
  32213400   314258017   346471417  159    202600    25417  1.0290886177  1.0340447422  Raab 2020
  39621748  1392332203  1431953951  223    177676    63067  1.0283440350  1.0296738675  Raab 2020
  16525824   233294389   249820213  159    103936    62005  1.0277069140  1.0312234078  Raab 2020
  31984512  1415477209  1447461721  192    166586   162553  1.0272143510  1.0282661105  Raab 2020
  31096700   113561549   144658249  145    214460   112209  1.0268341117  1.0394878515  Raab 2020
   9220500   192977791   202198291  125     73764    11167  1.0267758273  1.0291722818  Raab 2020
  13918926   697341727   711260653  177     78638    58581  1.0264518068  1.0273994434  Raab 2020
  11171584    36676693    47848277  151     73984    54613  1.0261177143  1.0407929736  Raab 2020
   7873524    78003593    85877117  114     69066    28079  1.0255655946  1.0307376110  Raab 2020
  42573010   802434421   845007431  215    198014    81693  1.0252749170  1.0277884791  Raab 2020
   6884640   618948611   625833251  180     38248    19475  1.0252706202  1.0257846030  Raab 2020
   7661402    26493569    34154971  127     60326    10455  1.0250310223  1.0392788572  Raab 2020
  63104964   348697267   411802231  186    339274   262869  1.0243014217  1.0326153144  Raab 2020
  21623824    12534133    34157957  152    142262    15077  1.0238135041  1.0750502453  Raab 2020
    411480   470669167   471080647  135      3048       55  1.0235488825  1.0235449993  Kourbatov/Wolf 2017
  12749892    32656489    45406381  159     80188    19973  1.0230264286  1.0411095632  Raab 2020
  22442616   201371617   223814233  189    118744   100537  1.0226532747  1.0280997629  Raab 2020
  68916000   139171757   208087757  150    459440   420877  1.0223790546  1.0425614834  Raab 2020
   2119706   665152001   667271707  211     10046     6341  1.0223668231  1.0224855590  Kourbatov/Wolf 2017
  10272212    33203981    43476193  158     65014    46841  1.0216006404  1.0364862243  Raab 2020
  94655398   250489231   345144629  191    495578   222341  1.0214682303  1.0373146802  Raab 2020
  15522600    19386091    34908691  150    103484    34583  1.0209911728  1.0526772896  Raab 2020
  21802200   139786609   161588809  150    145348   107181  1.0204493307  1.0279997768  Raab 2020
   5910084    51763573    57673657  102     57942    21367  1.0199911211  1.0258795038  Kourbatov/Wolf 2019
  15665628   140660603   156326231  121    129468    58355  1.0198122085  1.0253136814  Raab 2020
  30813000   182792257   213605257  125    246504   132793  1.0195126958  1.0274957358  Raab 2020
  33604510   154856431   188460941  185    181646    94039  1.0190978591  1.0292143015  Raab 2020
  31293030   908258651   939551681  145    215814   113339  1.0190659650  1.0206839169  Raab 2020
  50925936    58094497   109020433  113    450672   408481  1.0189432476  1.0504748177  Raab 2020
  62891296  1051239697  1114130993  221    284576    15953  1.0186773964  1.0214538133  Raab 2020
  13832418   724565069   738397487  201     68818    49165  1.0182064728  1.0191040049  Raab 2020
  56777754   267504733   324282487  113    502458   197077  1.0181853448  1.0278000222  Raab 2020
    657504   896016139   896673643  144      4566     2563  1.0179389550  1.0179401694  Kourbatov/Wolf 2017
  46246642   108866971   155113613  167    276926    35053  1.0173754306  1.0354406993  Raab 2020
  42567198   733564303   776131501  213    199846   129483  1.0166825429  1.0194136059  Raab 2020
   7326222   222677837   230004059  183     40034     8729  1.0166221904  1.0182458794  Kourbatov/Wolf 2019
   2823288    37906669    40729957  156     18098     9457  1.0162761199  1.0202123198  Kourbatov/Wolf 2017
   3185830  8337054667  8340240497  265     12022     2041  1.0157579142  1.0157635451  Raab 2020
   3923892  3025085407  3029009299  207     18956    11103  1.0148968246  1.0149380057  Raab 2020
    229350     1409633     1638983   55      4170      173  1.0145547849  1.0239918076  Kourbatov/Wolf 2017
   5450496   366870073   372320569  192     28388    11949  1.0140771094  1.0147754528  Kourbatov/Wolf 2019
  75525164   233697383   309222547  157    481052   387163  1.0140279077  1.0278960790  Raab 2020
   9639760   111124171   120763931  155     62192    49259  1.0138334837  1.0181940452  Raab 2020
  30930676    24205417    55136093  161    192116   190917  1.0134223607  1.0550102605  Raab 2020
  50418420   386155171   436573591  195    258556   131063  1.0133228991  1.0193961624  Raab 2020
  40721638    52043323    92764961  163    249826    79515  1.0128376956  1.0421613643  Raab 2020
  47941560    49222847    97164407   86    557460   166367  1.0125803645  1.0463002847  Raab 2020
  37405620   150807611   188213231   98    381690    40061  1.0125794282  1.0238363687  Raab 2020
  28110280    23247661    51357941  116    242330   226311  1.0124632857  1.0526838429  Raab 2020
  21274558  1705015261  1726289819  229     92902    77757  1.0124436726  1.0130055229  Raab 2020
  37123944   103922617   141046561  156    237974   165953  1.0122190047  1.0278829102  Raab 2020
 385368674    25348859   410717533  199   1936526   174021  1.0117855356  1.1024959563  Raab 2020
   7623726   160872571   168496297  121     63006    18253  1.0117585015  1.0141160813  Raab 2020
  19392048   104769641   124161689  108    179556    88493  1.0114121155  1.0202565037  Raab 2020
  17191872   931742089   948933961  144    119388    38137  1.0111387167  1.0119911112  Raab 2020
   2453760    11626561    14080321  135     18176    12097  1.0107626289  1.0218791350  Kourbatov/Wolf 2017
  43248460    98697649   141946109  139    311140    66269  1.0107319907  1.0291933253  Raab 2020
   3002682     8462609    11465291   89     33738    28109  1.0107025944  1.0283717872  Kourbatov/Wolf 2017
  20830992   285015677   305846669  156    133532    58389  1.0104842645  1.0140172971  Raab 2020
  37745708   153693563   191439271  143    263956    71171  1.0104329056  1.0215972900  Raab 2020
   1906050  4223927657  4225833707  131     14550     4457  1.0103872954  1.0103918943  Raab 2020
  56444996   994774373  1051219369  218    258922   254971  1.0103744227  1.0129958216  Raab 2020
   2937868    71725099    74662967  166     17698    12803  1.0103309882  1.0124218941  Kourbatov/Wolf 2017
   3108778   524646211   527754989  199     15622    12585  1.0098218219  1.0100720665  Kourbatov/Wolf 2017
  34340500   966299149  1000639649  173    198500     1149  1.0095741809  1.0112252851  Raab 2020
  27316160    26855831    54171991  160    170726    51849  1.0091149620  1.0450432633  Raab 2020
  38244528   216529571   254774099  126    303528   114107  1.0090204027  1.0171962322  Raab 2020
  21688044   406051133   427739177  107    202692    59057  1.0087753617  1.0113243560  Raab 2020
  25745040   747766631   773511671  162    158920    48031  1.0087685990  1.0103823236  Raab 2020
  25988580   496424063   522412643  102    254790    93143  1.0087199699  1.0111970717  Raab 2020
  46009194   501206653   547215847  159    289366    24741  1.0086176344  1.0128998671  Raab 2020
  47736960   152530297   200267257  115    415104   187129  1.0085751202  1.0222599621  Raab 2020
  15447230   354861707   370308937  157     98390    67367  1.0084080795  1.0105063318  Raab 2020
    532602      355339      887941   63      8454      271  1.0081862161  1.0661281933  Kourbatov/Wolf 2017
  13705524   244179227   257884751  126    108774    90371  1.0078434403  1.0105783718  Raab 2020
  20039880   715497919   735537799  140    143142    74203  1.0076771137  1.0089878396  Raab 2020
  40088160   132866873   172955033   82    488880   380393  1.0074523194  1.0207507645  Raab 2020
  58811344   820178353   878989697  212    277412   148481  1.0074489688  1.0107563320  Raab 2020
  16594812   285872417   302467229  118    140634   104129  1.0073862785  1.0101922452  Raab 2020
   7913376   366478501   374391877  129     61344     9445  1.0072590496  1.0082840851  Raab 2020
   6336090    10862323    17198413  135     46934    20569  1.0064940453  1.0322635782  Kourbatov/Wolf 2019
   1263426    10176791    11440217  129      9794      825  1.0056800570  1.0124473202  Kourbatov/Wolf 2017
  46050228   217133753   263183981  189    243652    39821  1.0055799493  1.0152019122  Raab 2020
  48286400   476773643   525060043  160    301790   247233  1.0053022416  1.0099987903  Raab 2020
  91995972   134314139   226310111  186    494602   276997  1.0051970084  1.0304647697  Raab 2020
   7044864   302145839   309190703  128     55038    42257  1.0048671503  1.0059802504  Kourbatov/Wolf 2019
  59879754   195127693   255007447  171    350174    80775  1.0047355186  1.0180212879  Raab 2020
   6580070     9659921    16239991  115     57218    47297  1.0046426332  1.0335781556  Kourbatov/Wolf 2019
  51467746    27521653    78989399  151    340846   253973  1.0046376418  1.0546436448  Raab 2020
  43509780   145858093   189367873   94    462870    54043  1.0045802322  1.0176743975  Raab 2020
1717149024     2144897  1719293921  144  11924646  2144897  1.0045650866  1.1079281784  Raab 2020
  13075056     1108727    14183783   87    150288    56711  1.0044797434  1.1084765832  Raab 2020
  13439592  1168184821  1181624413  146     92052    44941  1.0040622170  1.0045775514  Raab 2020
  28352916    35142521    63495437  162    175018   138921  1.0037465003  1.0340546108  Raab 2020
  21976512   549084871   571061383  204    107728   102983  1.0037234187  1.0056145476  Raab 2020
  29832516   238445833   268278349  189    157844   101393  1.0036031644  1.0095146956  Raab 2020
  36180210   145871087   182051297  165    219274    53877  1.0035484669  1.0147724824  Raab 2020
  40408416   986864401  1027272817  216    187076    38501  1.0033433424  1.0052328333  Raab 2020
  33483000   215811593   249294593  150    223220   181073  1.0032754840  1.0105108305  Raab 2020
   4358676   456043963   460402639  133     32772    21583  1.0031136169  1.0035397670  Raab 2020
  31133600   439349837   470483437  200    155668    54741  1.0031057406  1.0064506471  Raab 2020
  27551940   338556937   366108877  195    141292    21305  1.0030711445  1.0069378649  Raab 2020
  15331396   565558423   580889819  202     75898    42425  1.0029708311  1.0042463480  Raab 2020
  23412288   175749583   199161871  183    127936    93455  1.0027528576  1.0091045460  Raab 2020
   1594416   145465687   147060103  118     13512     9007  1.0026889378  1.0031790166  Kourbatov/Wolf 2017
  10861720   838264771   849126491  164     66230    57891  1.0024939750  1.0030815954  Raab 2020
   2306938    82541821    84848759  167     13814     3171  1.0022590147  1.0036450169  Kourbatov/Wolf 2017
  62453988    21427013    83881001  153    408196   200821  1.0022380684  1.0635856005  Raab 2020
  17885700  1540935449  1558821149  153    116900    76549  1.0019820978  1.0024980415  Raab 2020
  20569432   769650307   790219739  194    106028    99083  1.0018790832  1.0031212916  Raab 2020
  39889386    27538787    67428173  107    372798   324533  1.0017029036  1.0452937817  Raab 2020
  12379428   663185953   675565381  138     89706    79201  1.0016346146  1.0024974574  Raab 2020
  24229590   583703311   607932901  165    146846   137307  1.0015954952  1.0035453014  Raab 2020
  43562550     1901563    45464113   83    524850   327013  1.0014031914  1.1083793957  Raab 2020
  20149566   393144877   413294443  127    158658   149011  1.0013961710  1.0038325361  Raab 2020
  12923460    84117277    97040737  110    117486   114787  1.0013287456  1.0087976608  Raab 2020
     54264  825353008489 ...062753  357       152       33  1.0010143609  1.0010132538  Raab 2020
  47797860    29115551    76913411  110    434526     2309  1.0008633483  1.0472594243  Raab 2020
  25487000   313905113   339392113  140    182050    50913  1.0008612832  1.0047158319  Raab 2020
  19510266   489350311   508860577  201     97066    40605  1.0002453898  1.0021310501  Raab 2020
  26869948    20920033    47789981  134    200522    65745  1.0000761994  1.0415155353  Raab 2020
   1885228   163504573   165389801  179     10532     5805  1.0000704209  1.0005917231  Kourbatov/Wolf 2017
   3758772   144803717   148562489  118     31854    27287  1.0000152764  1.0012763548  Kourbatov/Wolf 2017

Next goal: CSG > A201559
Attached Files
File Type: pdf factorizations1.pdf (415.0 KB, 73 views)
File Type: pdf factorizations2.pdf (418.4 KB, 75 views)
mart_r is offline   Reply With Quote
Old 2020-06-10, 15:11   #20
mart_r
 
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Dec 2008
you know...around...

25·19 Posts
Exclamation Mind the gap!

A killing sieve at work:

Code:
g = 99,754,416
p = 397,778,383
q = 615,768 = 2³ × 3 × 25,657
phi(q) = 205,248
k = 162
g / [phi(q) log²(p')] = 1.21199459979...
Sum Ri'(x) method = 1.2250203518...
Merit = 24.40047328...
(2020-06-10)

397778383 = 397778383
398394151 = 293 x 773 x 1759
399009919 = 7 x 11 x 5181947
399625687 = 79 x 461 x 10973
400241455 = 5 x 17 x 89 x 191 x 277
400857223 = 13 x 37 x 43 x 19381
401472991 = 10331 x 38861
402088759 = 61 x 6591619
402704527 = 29 x 13886363
403320295 = 5 x 7 x 23 x 501019
403936063 = 3709 x 108907
404551831 = 389 x 1039979
405167599 = 10987 x 36877
405783367 = 11 x 3491 x 10567
406399135 = 5 x 151 x 193 x 2789
407014903 = 19 x 31 x 103 x 6709
407630671 = 7 x 47 x 1238999
408246439 = 53 x 7702763
408862207 = 13 x 13 x 67 x 36109
409477975 = 5 x 5 x 16379119
410093743 = 149 x 2752307
410709511 = 17 x 71 x 227 x 1499
411325279 = 6899 x 59621
411941047 = 7 x 557 x 105653
412556815 = 5 x 11 x 7501033
413172583 = 887 x 465809
413788351 = 12239 x 33809
414404119 = 373 x 709 x 1567
415019887 = 317 x 1309211
415635655 = 5 x 41 x 41 x 49451
416251423 = 7 x 7 x 7 x 1213561
416867191 = 13 x 32066707
417482959 = 23 x 18151433
418098727 = 263 x 761 x 2089
418714495 = 5 x 19 x 73 x 173 x 349
419330263 = 11 x 38120933
419946031 = 11981 x 35051
420561799 = 7 x 29 x 2071733
421177567 = 17 x 487 x 50873
421793335 = 5 x 4643 x 18169
422409103 = 7607 x 55529
423024871 = 9497 x 44543
423640639 = 37 x 11449747
424256407 = 457 x 928351
424872175 = 5 x 5 x 7 x 13 x 186757
425487943 = 839 x 507137
426103711 = 11 x 31 x 197 x 6343
426719479 = 5881 x 72559
427335247 = 43 x 1889 x 5261
427951015 = 5 x 409 x 209267
428566783 = 1487 x 288209
429182551 = 7 x 4861 x 12613
429798319 = 83 x 257 x 20149
430414087 = 19 x 157 x 144289
431029855 = 5 x 331 x 260441
431645623 = 17 x 23 x 401 x 2753
432261391 = 97 x 127 x 35089
432877159 = 11 x 13 x 59 x 51307
433492927 = 7 x 61927561
434108695 = 5 x 86821739
434724463 = 17929 x 24247
435340231 = 241 x 829 x 2179
435955999 = 1861 x 234259
436571767 = 47 x 719 x 12919
437187535 = 5 x 87437507
437803303 = 7 x 2579 x 24251
438419071 = 29 x 15117899
439034839 = 7013 x 62603
439650607 = 11 x 61 x 643 x 1019
440266375 = 5 x 5 x 5 x 3522131
440882143 = 13 x 41 x 53 x 15607
441497911 = 569 x 775919
442113679 = 7 x 17 x 19 x 195539
442729447 = 1129 x 392143
443345215 = 5 x 7919 x 11197
443960983 = 167 x 2658449
444576751 = 179 x 2483669
445192519 = 31 x 14361049
445808287 = 23 x 991 x 19559
446424055 = 5 x 7 x 7 x 11 x 11 x 11 x 37 x 37
447039823 = 1201 x 372223
447655591 = 1367 x 327473
448271359 = 79 x 397 x 14293
448887127 = 13 x 101 x 341879
449502895 = 5 x 593 x 151603
450118663 = 67 x 113 x 59453
450734431 = 7 x 64390633
451350199 = 137 x 3294527
451965967 = 107 x 4223981
452581735 = 5 x 17 x 5324491
453197503 = 11 x 41199773
453813271 = 19 x 43 x 251 x 2213
454429039 = 71 x 859 x 7451
455044807 = 7 x 89 x 109 x 6701
455660575 = 5 x 5 x 131 x 139133
456276343 = 29 x 15733667
456892111 = 13 x 35145547
457507879 = 229 x 1997851
458123647 = 21317 x 21491
458739415 = 5 x 2383 x 38501
459355183 = 7 x 367 x 178807
459970951 = 11 x 23 x 1818067
460586719 = 13367 x 34457
461202487 = 19319 x 23873
461818255 = 5 x 2749 x 33599
462434023 = 14447 x 32009
463049791 = 17 x 27238223
463665559 = 7 x 73 x 907369
464281327 = 31 x 1483 x 10099
464897095 = 5 x 13 x 7152263
465512863 = 19 x 47 x 547 x 953
466128631 = 41 x 239 x 47569
466744399 = 11 x 1867 x 22727
467360167 = 12409 x 37663
467975935 = 5 x 7 x 379 x 35279
468591703 = 4349 x 107747
469207471 = 37 x 59 x 59 x 3643
469823239 = 6619 x 70981
470439007 = 103 x 4567369
471054775 = 5 x 5 x 18842191
471670543 = 9371 x 50333
472286311 = 7 x 67469473
472902079 = 13 x 877 x 41479
473517847 = 11 x 17 x 53 x 47777
474133615 = 5 x 23 x 29 x 142169
474749383 = 223 x 233 x 9137
475365151 = 2819 x 168629
475980919 = 14411 x 33029
476596687 = 7 x 7 x 9726463
477212455 = 5 x 19 x 61 x 82349
477828223 = 3001 x 159223
478443991 = 1489 x 321319
479059759 = 181 x 281 x 9419
479675527 = 307 x 443 x 3527
480291295 = 5 x 11 x 43 x 311 x 653
480907063 = 7 x 13 x 83 x 63671
481522831 = 8387 x 57413
482138599 = 613 x 757 x 1039
482754367 = 139 x 3473053
483370135 = 5 x 31 x 269 x 11593
483985903 = 17 x 28469759
484601671 = 20963 x 23117
485217439 = 7 x 971 x 71387
485833207 = 491 x 989477
486448975 = 5 x 5 x 19457959
487064743 = 11 x 44278613
487680511 = 13001 x 37511
488296279 = 23 x 21230273
488912047 = 13 x 19 x 19 x 104179
489527815 = 5 x 7 x 13986509
490143583 = 11551 x 42433
490759351 = 10891 x 45061
491375119 = 41 x 67 x 178877
491990887 = 29 x 29 x 37 x 97 x 163
492606655 = 5 x 2971 x 33161
493222423 = 7841 x 62903
493838191 = 7 x 11 x 6413483
494453959 = 17 x 47 x 618841
495069727 = 2267 x 218381
495685495 = 5 x 99137099
496301263 = 7559 x 65657
496917031 = 13 x 79 x 483853
497532799 = 497532799
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Old 2020-06-19, 16:57   #21
Bobby Jacobs
 
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Is this gap the largest CSG known for a prime gap in residues?
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Old 2020-06-19, 19:12   #22
mart_r
 
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As far as I know, it is.
I'm not aware of any gap with a larger CSG value.
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