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Old 2019-12-18, 15:18   #31
kriesel
 
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"TF79LL86GIMPS96gpu17"
Mar 2017
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Default P-1 selftest candidates

P-1 factoring software lacks built-in selftest capability. The P-1 algorithm is possibly checkable in portions of the computations with the 50% error detection probability Jacobi symbol, although at higher computational cost than for the LL test, because the correct symbol and the obtained symbol must both be computed. That cost must be weighed against the smaller potential time savings possible by detecting an error in a P-1 computation. P-1 factoring is of order 30 times less time consuming than a primality test for the same exponent. Currently, no GIMPS P-1 factoring software includes any Jacobi check, other than Gpuowl v7.x, in stage 1.

For now, the available method of checking reliability of P-1 factoring software and hardware combination is to run multiple exponents with known factors. It's recommended to perform a self-test for each combination in use at least annually, at installation, and upon change of configuration. Following are some candidates for such self-test. Good self test candidates have known factors that will require large enough B2 that both stages will be exercised, but not bounds so large that run time is intractably long, and if they have multiple factors, ideally all factors have compatible bounds so that the run does not terminate in stage 1 and all known factors can be confirmed found. That must include the effect of some versions of gpuowl and Mlucas imposing minimums on stage 1 bound, such as 15015 in gpuowl v6.11-380; 10000 in gpuowl v7.2-86; 10000 in Mlucas v20.1.1.

Note, the larger ones <1G can take several days, even in Gpuowl on a Radeon VII, and some above 1G may be too large for gpuowl and require Mlucas V20.x on a fast many core CPU and run times of months or years each for normal bounds. Maximum feasible exponent is a function of both software and hardware. See the relevant P-1-supporting applications' reference threads for some indications of what's possible for each.

Exponents, bounds required, etc.
Code:
    Exponent      Min B1         Min B2     fft length         notes
    1,000,099        107         350,179      48k
    3,000,077       7669       1,166,483     160k
    4,444,091          7           2,557     256k
   10,000,831     29,173         492,251    ?
   24,000,577          1         281,339    ?
   30,000,853          1           75011    1664k
   50,001,781     94,709       4,067,587    2688k
   51,558,151      5,953       2,034,041    2880k
   54,447,193      1,181         682,009    3072k
   58,610,467     70,843         694,201    3200k
   61,012,769     10,273       1,572,097    3360k    
   81,229,789      6,709      11,282,221    4704K    
  100,000,081      1,289       7,554,653    5600K  
  110,505,011    114,967       8,616,197    6144K
  120,002,191      1,563       3,109,391    7168K    
  150,000,713     15,131       2,294,519    8640K    
  200,000,183        953       1,138,061   11200K        
  200,001,187    204,983         207,821   11200K    
  200,003,173      4,651         229,813   11200K  
  230,086,243    321,547         417,541   ?
  249,500,221          4   2,589,507,467   14336K    
  249,500,501        307         167,381   14336K    
  290,001,377      2,551      34,354,769   16384K
  300,008,497          8           41161   16384k
  301,000,159      1,499       8,999,819   18432K
  332,230,189    343,289       5,552,263   18816K
  353,466,917     27,299       7,831,403   ?
  407,363,239    508,103      10,407,589   23040K
  423,000,089      9,221      73,375,433   24192K
  464,000,021      3,229      63,576,391   ?
  490,000,003  1,126,523      458,98,729   ?
  502,000,027     13,777       1,099,081   28672K
  563,021,377    105,253  14,013,184,573   ?
  640,402,457    224,699       4,574,429   ?
  654,036,583        101   9,507,343,133   ?
  745,964,951       2617            7963   ?
  840,859,433        787       1,327,871   ?
  901,000,031  1,362,211      22,449,467   51840K
  940,216,091    269,393   6,481,528,541   ?
  980,000,521    211,777      61,117,579   ?
1,100,000,081        499         168,673
1,138,000,001  2,178,791      12,199,907
1,199,999,579         37         385,573
1,299,999,919          8          18,013   72M
1,414,000,001         11         432,281
1,552,999,957        107          16,787
1,553,000,003         41 516,417,465,401
1,553,000,143          1          21,317
1,708,000,339         27      40,617,119   or B1=14843, B2=26209
1,862,000,159       1693      33,292,423
2,000,000,089       2029          69,149
3,321,928,601        241 185,131,571,099   192M (stage 2 run time would be very long)
3,321,928,619         37       2,442,599   192M
3,321,928,703        107          73,181   192M
3,321,928,787        907         188,171   192M
3,330,000,293       8620          61,441
4,000,000,229        197          31,333
4,294,967,111        151       4,277,333
4,294,967,357       9293            9293   256M
6,330,000,829          7          10,781
8,230,000,949          3         104,311
8,883,334,777        947          15,887
9,993,000,001         59              79
CUDAPm1 format worktodo lines:
Code:
PFactor=1,2,1000099,-1,67,2
PFactor=1,2,3000077,-1,67,2
PFactor=1,2,4444091,-1,70,2
PFactor=1,2,10000831,-1,68,2
PFactor=1,2,24000577,-1,70,2
PFactor=1,2,30000853,-1,67,2
PFactor=1,2,50001781,-1,74,2
PFactor=1,2,51558151,-1,74,2
PFactor=1,2,54447193,-1,74,2
PFactor=1,2,58610467,-1,74,2
PFactor=1,2,61012769,-1,74,2
PFactor=1,2,81229789,-1,75,2
PFactor=1,2,100000081,-1,76,2
PFactor=1,2,110505011,-1,76,2
PFactor=1,2,120002191,-1,77,2
PFactor=1,2,150000713,-1,77,2
PFactor=1,2,200001187,-1,79,2
PFactor=1,2,230086243,-1,79,2
PFactor=1,2,249500501,-1,79,2
PFactor=1,2,290001377,-1,80,2
PFactor=1,2,300008497,-1,80,2
PFactor=1,2,301000159,-1,80,2
PFactor=1,2,332230189,-1,81,2
PFactor=1,2,353466917,-1,81,2
PFactor=1,2,407363239,-1,81,2
PFactor=1,2,423000089,-1,82,2
PFactor=1,2,464000021,-1,82,2
PFactor=1,2,490000003,-1,82,2
PFactor=1,2,502000027,-1,82,2
PFactor=1,2,563021377,-1,81,2
PFactor=1,2,640402457,-1,84,2
PFactor=1,2,654036583,-1,84,2
PFactor=1,2,745964951,-1,84,2
PFactor=1,2,840859433,-1,83,2
PFactor=1,2,901000031,-1,85,2
PFactor=1,2,940216091,-1,85,2
PFactor=1,2,980000521,-1,78,2
PFactor=1,2,1100000081,-1,68,2
PFactor=1,2,1138000001,-1,80,2
PFactor=1,2,1199999579,-1,68,2
PFactor=1,2,1299999919,-1,68,2
PFactor=1,2,1414000001,-1,87,2
PFactor=1,2,1552999957,-1,87,2
PFactor=1,2,1553000003,-1,87,2
PFactor=1,2,1553000143,-1,87,2
PFactor=1,2,1708000339,-2,88,2
PFactor=1,2,1862000159,-1,88,2
PFactor=1,2,2000000089,-1,89,2
PFactor=1,2,3321928601,-1,91,2
PFactor=1,2,3321928619,-1,91,2
PFactor=1,2,3321928703,-1,91,2
PFactor=1,2,3321928787,-1,91,2
PFactor=1,2,3330000293,-1,91,2
PFactor=1,2,4000000229,-1,92,2
PFactor=1,2,4294967111,-1,92,2
PFactor=1,2,4294967357,-1,92,2
PFactor=1,2,6330000829,-1,94,2
PFactor=1,2,8230000949,-1,96,2
PFactor=1,2,8883334777,-1,96,2
PFactor=1,2,9993000001,-1,96,2
Mlucas v20.x format worktodo lines:
Code:
PMinus1=00000000000000000000000000000000,1,2,1000099,-1,107,350179
PMinus1=00000000000000000000000000000000,1,2,3000077,-1,8000,1200000
PMinus1=00000000000000000000000000000000,1,2,10000019,-1,409,4331947
PMinus1=00000000000000000000000000000000,1,2,10000831,-1,29173,492251
PMinus1=00000000000000000000000000000000,1,2,30000853,-1,1,75011
PMinus1=00000000000000000000000000000000,1,2,100000193,-1,479,5973637
PMinus1=00000000000000000000000000000000,1,2,300008497,-1,8,41161
PMinus1=00000000000000000000000000000000,1,2,502000027,-1,13777,1099081
PMinus1=00000000000000000000000000000000,1,2,745964951,-1,2617,7963
PMinus1=00000000000000000000000000000000,1,2,980000521,-1,211777,61117579
PMinus1=00000000000000000000000000000000,1,2,1100000081,-1,499,168673
PMinus1=00000000000000000000000000000000,1,2,1138000001,-1,2178791,12199907
PMinus1=00000000000000000000000000000000,1,2,1199999579,-1,37,385573
PMinus1=00000000000000000000000000000000,1,2,1299999919,-1,8,18013
PMinus1=00000000000000000000000000000000,1,2,1414000001,-1,11,432281
PMinus1=00000000000000000000000000000000,1,2,1552999957,-1,107,16787
PMinus1=00000000000000000000000000000000,1,2,1553000003,-1,41,516417465401
PMinus1=00000000000000000000000000000000,1,2,1553000143,-1,1,21317
PMinus1=00000000000000000000000000000000,1,2,1708000339,-1,27,40617119
PMinus1=00000000000000000000000000000000,1,2,1862000159,-1,1693,33292423
PMinus1=00000000000000000000000000000000,1,2,2000000089,-1,2029,69149
PMinus1=00000000000000000000000000000000,1,2,3321928619,-1,37,2442599
PMinus1=00000000000000000000000000000000,1,2,3321928703,-1,107,73181
PMinus1=00000000000000000000000000000000,1,2,3321928787,-1,907,188171
PMinus1=00000000000000000000000000000000,1,2,3330000293,-1,8620,61441
PMinus1=00000000000000000000000000000000,1,2,4000000229,-1,197,31333
PMinus1=00000000000000000000000000000000,1,2,4294967111,-1,151,4277333
PMinus1=00000000000000000000000000000000,1,2,4294967357,-1,9293,9293
PMinus1=00000000000000000000000000000000,1,2,6330000829,-1,7,10781
PMinus1=00000000000000000000000000000000,1,2,8230000949,-1,3,104311
PMinus1=00000000000000000000000000000000,1,2,8883334777,-1,947,15887
PMinus1=00000000000000000000000000000000,1,2,9993000001,-1,59,79
Factors that should be found:
Code:
Exponent    Factor (may be composite)    Prime factors
 1000099    155058493988826487335266033969 = 1872347344039 x 82815026005984871
 3000077    10235118022140996045023873
 4444091    1809798096458971047321927127  = 8888183 * 319974553 * 636358278473
10000831    646560662529991467527
24000577    13504596665207
30000853    4500787968767
50001781    4392938042637898431087689
51558151    55277543419074012358186647    
54447193    17261184235049628259201
58610467    69057033982979789260999
61012769    2018028590362685212673
81229789    355078783674010195200030259699844128700274440385857 
        =   488121804389130135740149369 * 727438890213848757119753
100000081   3441393510714285782119
110505011   135956751441091446931829737
120002191   100835659918276033441
150000713   1447762785107694357647
200000183   849003842550205126847    
200001187   3050161780881530584679
200003173   14652109287435525414352647642348599 
                 = 4320552944485007 * 3391257895852957657
230086243   155914837698663336739324225993
249500221   5168661482381201657 
249500501   3571511465549660434777661921959439 
                = 11607130072256471 * 307699788260867209
290001377   10645243382592701071676802590718709559 
                = 1436135993277492383 * 7412420155488583273
    or 90944796249039267769901814723364335322839708522092302667497 =
     170370076089478747961  * 371696926552024067119 * 1436135993277492383
300008497   1422604742689454023244777 = 4800135953 * 296367593880409
301000159   99812588622057998165480647
332230189   400336212296331535712337247
353466917   32645162170211204627569
407363239   2460083406159745463265647
423000089   7999281314567748179722151
464000021   56208073342032516397974073
490000003   70426817562272964022712873527
502000027   2107472748472812989445447752584121
563021377   4982501757616947169867879
640402457   252244080831943611399099691087    
654036583   45218388371594348767609
745964951   87913098632237818693849
840859433   15173015946721772325308641
901000031   266276073654639633298220609
940216091   3283382049964706665517567
980000521   507377532831334081081721
1100000081  5714844092575663518975201100656679 = 3429201852513937 * 1666523097316691767
1138000001  7594538416378952702754560188879
1199999579  5341263780505966249
1299999919   1124011129965457
1414000001  282395344507713823
1552999957  20546431193021757889009340641793 = 27279997244663 * 753168374936013511
1553000003  65763698675994442488647
1553000143  66210608096663
1708000339  194802340883538981529 or 19072275530004400752673 or f1 * f2 =
      3715323919220696374139018576724663444377017
1862000159  629699467708232820607
2000000089  2244853235895964553
3321928601  257595098623128649646526143
3321928619  2293064264678630032768684192802141895628004057
           = 797262868561 * 48684837137044687 * 59077344656726951
3321928703  115332226795467793458711160224636005176709611559
           = 2577816673529 * 558801558703849 * 80064692506573275079
3321928787  108855788204768513089
3330000293  1412384696568876781601
4000000229  543188919097563839
4294967111  372306737694762380303561
4294967357  66351306085844627044301094631 = 34359738857 * 1931077135422613583
6330000829  26751545663480009
8230000949  15452633321840503
8883334777  490761602940053167417
9993000001  34737975328983194714064620017 = 4616766000463 * 7524309294752959
(We need more coverage of the mersenne.org space, and mersenne.ca space, with modest ratios between successive sorted exponents, to provide scattered coverage across the fft size and memory requirements range. For factors that can be found with normal gpu72 or PrimeNet bounds. If you know of any, please PM kriesel with them)


Top of this reference thread: https://www.mersenneforum.org/showpo...89&postcount=1
Top of reference tree: https://www.mersenneforum.org/showpo...22&postcount=1

Last fiddled with by kriesel on 2022-04-24 at 18:52 Reason: added a >8G test candidate
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