P-1 discussion thread

[philmoore]

Here is the complete list, although Rincewind still has about 50 candidates to test, so we could possibly add one or two to this list of 23 factors so far:

2^6261832+40291 has a factor: 218625843059160319 (57.6 bits)
F-1 = 2 * 3^2 * 47 * 211 * 383 * 443 * 1381 * 5227 (stage 1)
2^6265432+40291 has a factor: 26315751200625979 (54.5 bits)
F-1 = 2 * 3 * 7 * 13 * 43 * 59 * 401 * 733 * 64633
2^6286456+40291 has a factor: 6830498069971913 (52.6 bits)
F-1 = 2^3 * 7 * 29 * 73 * 167 * 263 * 307 * 4273 (stage 1)
2^6391720+40291 has a factor: 3569076525442609 (51.7 bits)
F-1 = 2^4 * 3^2 * 19 * 43 * 137 * 12109 * 18287 (stage 1)
2^6411688+40291 has a factor: 252938575558541129923 (67.8 bits)
F-1 = 2 * 3^4 * 7 * 41 * 47 * 79 * 929 * 17597 * 89627
2^6463336+40291 has a factor: 56617484284072273 (55.7 bits)
F-1 = 2^4 * 3 * 11 * 739 * 1901 * 4733 * 16127 (stage 1)
2^6474856+40291 has a factor: 1705720144293691 (50.6 bits)
F-1 = 2 * 3 * 5 * 7 * 19^2 * 37 * 61 * 503 * 19819 (stage 1)
2^6491992+40291 has a factor: 17297421582358339 (53.9 bits)
F-1 = 2 * 3 * 31 * 1877 * 2003 * 4691 * 5273 (stage 1)
2^6525064+40291 has a factor: 32903761423968667 (54.9 bits)
F-1 = 2 * 3^3 * 7^2 * 11 * 2251 * 4759 * 105529
2^6535624+40291 has a factor: 655327786132738732241 (69.2 bits)
F-1 = 2^4 * 5 * 19 * 421 * 1117 * 3499 * 4013 * 65293
2^6559048+40291 has a factor: 130736121764993011 (56.9 bits)
F-1 = 2 * 3^3 * 5 * 7 * 199 * 499 * 18061 * 38569
2^6642712+40291 has a factor: 5595285582536917 (52.3 bits)
F-1 = 2^2 * 3 * 7 * 19 * 41 * 421 * 10457 * 19423 (stage 1)
2^6730984+40291 has a factor: 24036632157302523931 (64.4 bits)
F-1 = 2 * 3 * 5 * 73 * 677 * 8761 * 15749 * 117499
2^6774376+40291 has a factor: 43725292271979907 (55.3 bits)
F-1 = 2 * 3 * 7^2 * 17 * 31 * 1399 * 7547 * 26729
2^6784072+40291 has a factor: 6370042811545733 (52.5 bits)
F-1 = 2^2 * 11 * 23 * 367 * 991 * 2341 * 7393 (stage 1)
2^6842536+40291 has a factor: 24019691081440807609 (64.4 bits)
F-1 = 2^3 * 3 * 19 * 151 * 719 * 1627 * 6311 * 47251
2^6872104+40291 has a factor: 64082456520814183 (55.8 bits)
F-1 = 2 * 3 * 11 * 17 * 41 * 233 * 257 * 1619 * 14369 (stage 1)
2^6973192+40291 has a factor: 45073638202056239 (55.3 bits)
F-1 = 2 * 43 * 47 * 131 * 461 * 6263 * 29483
2^6982984+40291 has a factor: 287491350230855681 (58.0 bits)
F-1 = 2^12 * 5 * 7 * 13^2 * 59 * 2111 * 95273
2^7022872+40291 has a factor: 1481731544880157 (50.4 bits)
F-1 = 2^2 * 3 * 29 * 463 * 557 * 1009 * 16363 (stage 1)
2^7074472+40291 has a factor: 22172835407089501 (54.3 bits)
F-1 = 2^2 * 3^4 * 5^3 * 7 * 521 * 1103 * 136099
2^7101160+40291 has a factor: 4064266716413669 (51.9 bits)
F-1 = 2^2 * 31 * 97 * 103^2 * 271 * 117529
2^7175224+40291 has a factor: 153966748432113121 (57.1 bits)
F-1 = 2^5 * 3 * 5 * 7^2 * 8059 * 11681 * 69539

Given that our current sieving depth is between 50.1 and 50.3 bits, we have probably saved 22 first time tests, and maybe 16 double checks if we eventually get that far. I am struck by the fact that 10 of these factors showed up in stage 1, and that even lowering the B1 and B2 limits by 20% would not have excluded a single factor! P-1 factoring time to given limits will go up approximately as the number of bits (digits), while PRP testing time will go up approximately as the square of the number of bits (digits), so we will eventually increase the B1 and B2 limits, but this seems to be a pretty effective level at the moment (B1 = 25000, B2 = 200000). I was expecting maybe 15 or 16 factors based on the Prime95 estimate, so I hope that the estimate was simply too conservative.

[Rincewind]

This is realy great!
My range is nearly finished (5 tests to go).
EDIT: should take about 2 hours.

[philmoore]

Christian (Rincewind) and I have found the following factors in the range 7.2-7.6M:

2^7346584+40291 has a factor: 2713575839646593 (51.3 bits)
F-1 = 2^7 * 23 * 37 * 61 * 107 * 257 * 14851
2^7377736+40291 has a factor: 3372333924960107 (51.6 bits)
F-1 = 2 * 181 * 2593 * 15901 * 225941
2^7431112+40291 has a factor: 647238388043868157 (59.2 bits)
F-1 = 2^2 * 3^2 * 19 * 241 * 3719 * 7759 * 136069
2^7452280+40291 has a factor: 72361607863067671 (56.0 bits)
F-1 = 2 * 3 * 5 * 7 * 41 * 47 * 101 * 113 * 2591 * 6047
2^7459480+40291 has a factor: 12196062014091841 (53.4 bits)
F-1 = 2^6 * 3^4 * 5 * 23 * 307 * 6553 * 10169
2^7468648+40291 has a factor: 2074486548895391 (50.9 bits)
F-1 = 2 * 5 * 7 * 881 * 1459 * 2749 * 8387
2^7473928+40291 has a factor: 37120355543104181 (54.0 bits)
F-1 = 2^2 * 5 * 787 * 1103 * 24023 * 89003
2^7481128+40291 has a factor: 10838140836939841 (53.3 bits)
F-1 = 2^6 * 3 * 5 * 197 * 421 * 8849 * 15383
2^7482904+40291 has a factor: 64263545688466413073 (65.8 bits)
F-1 = 2^4 * 3^3 * 7 * 97 * 277 * 281 * 13147 * 214091
2^7506904+40291 has a factor: 3437657820791533 (51.6 bits)
F-1 = 2^2 * 3^4 * 13^2 * 19 * 193 * 569 * 30089
2^7581016+40291 has a factor: 1235188749289504717 (60.1 bits)
F-1 = 2^2 * 3^2 * 7^2 * 419 * 1913 * 7883 * 110819

He was unlucky in finding none in the 7.2-7.3M range, but I made up for it by finding seven in the 7.4-7.5M range. I'll update the work files.

[philmoore]

More factors:

2^7399336+40291 has a factor: 184823073514334401 (57.4 bits)
F-1 = 2^6 * 3 * 5^2 * 17 * 107 * 491 * 3041 * 14177
2^7612264+40291 has a factor: 6024221035441019 (52.4 bits)
F-1 = 2 * 31 * 347 * 1447 * 10567 * 18313
2^7623304+40291 has a factor: 1743744885927229 (50.6 bits)
F-1 = 2^2 * 3^2 * 269 * 1571 * 9439 * 12143
2^7704616+40291 has a factor: 2323574065780073 (51.0 bits)
F-1 = 2^3 * 7 * 59 * 67 * 739 * 1777 * 7993
2^7730344+40291 has a factor: 5065691636151879721 (62.1 bits)
F-1 = 2^3 * 3 * 5 * 13 * 661 * 691 * 701 * 2467 * 4111
2^7798552+40291 has a factor: 25556456239246213 (51.2 bits)
F-1 = 2^2 * 3 * 7^2 * 107 * 229 * 239 * 419 * 17713

Several are not far beyond our current factoring range. What I thought was interesting is that none of these factors required stage 2. I'll remove these and upload new work (prp) files soon.

[engracio]

Wow! Up to 9.11m already and all I got is a whopping 1 factor. We're cooking now boys.

[engracio]

Originally Posted by engracio

Wow! Up to 9.11m already and all I got is a whopping 1 factor. We're cooking now boys.

Never mind soon as I posted this, within the hour two factors popped one after the other.

[engracio]

Completed 9.0m-9.5m, 13 factors found. Request 10.0m-11.0m.

2^9056104+40291 has a factor: 2481405372790507301
2^9104440+40291 has a factor: 49080523497812502529
2^9117064+40291 has a factor: 11666987687599789
2^9118840+40291 has a factor: 2837545094114309
2^9146152+40291 has a factor: 30424904484696329
2^9147688+40291 has a factor: 1867847549389889
2^9164056+40291 has a factor: 2951666932144921
2^9189880+40291 has a factor: 383745046407932873
2^9196744+40291 has a factor: 194199257370309083
2^9329800+40291 has a factor: 124140830241515587
2^9355000+40291 has a factor: 40293425732611801
2^9397624+40291 has a factor: 11213210689080853
2^9431224+40291 has a factor: 58651135088627651

[engracio]

Completed 9.5m-10.0m, 24 factors found.

2^9532744+40291 has a factor: 11831525764370497
2^9553240+40291 has a factor: 6542993566612513
2^9555496+40291 has a factor: 136126041570036961
2^9576904+40291 has a factor: 353646830365785857
2^9593320+40291 has a factor: 2515265092622857
2^9611176+40291 has a factor: 1877012631379153
2^9633592+40291 has a factor: 201824734382727641
2^9651448+40291 has a factor: 12911043723845871299
2^9652264+40291 has a factor: 14498940614584289
2^9679432+40291 has a factor: 3571587617874013
2^9703096+40291 has a factor: 28433764153180123
2^9711160+40291 has a factor: 45074219486837936257
2^9745048+40291 has a factor: 26450419580594803
2^9765976+40291 has a factor: 2444324883242119
2^9794248+40291 has a factor: 6760975234917661
2^9807496+40291 has a factor: 37971266118158357
2^9826792+40291 has a factor: 62352316322273110829
2^9854104+40291 has a factor: 11196672058290941
2^9856360+40291 has a factor: 5298322715405663
2^9860872+40291 has a factor: 139959018203857711
2^9883480+40291 has a factor: 15043934158575617
2^9895960+40291 has a factor: 13391071515242131
2^9906472+40291 has a factor: 14275270738920913321
2^9917176+40291 has a factor: 21750890144935529

[engracio]

Completed 10.0m-11.0m, 15 factors found.

2^10055944+40291 has a factor: 12940672966841057
2^10111240+40291 has a factor: 30302090108450053
2^10177288+40291 has a factor: 2790996575702591
2^10298440+40291 has a factor: 94991333981885287
2^10441432+40291 has a factor: 20045778961224761
2^10587304+40291 has a factor: 45035371651253237
2^10592344+40291 has a factor: 2558581450444709
2^10611208+40291 has a factor: 2285644830758613689
2^10642312+40291 has a factor: 40225360865931107
2^10740616+40291 has a factor: 134172909421356059
2^10780072+40291 has a factor: 8453719162878329
2^10780696+40291 has a factor: 40214211520234727141
2^10797880+40291 has a factor: 779054456279048677171
2^10869016+40291 has a factor: 632161424389032983
2^10872040+40291 has a factor: 11924085367056787

e

[engracio]

Completed 11m-12m, 42 factors found.

2^11005432+40291 has a factor: 10051333853031845639
2^11015128+40291 has a factor: 37359123714127751
2^11041384+40291 has a factor: 70431316822641457
2^11120728+40291 has a factor: 4140033775067537
2^11154376+40291 has a factor: 1386144990568879789
2^11165800+40291 has a factor: 5319712758883093
2^11221192+40291 has a factor: 1668931804844309
2^11231608+40291 has a factor: 1964344549730711
2^11254888+40291 has a factor: 4975729140906779
2^11313352+40291 has a factor: 22660703964351045181
2^11322808+40291 has a factor: 5514127900903591
2^11426968+40291 has a factor: 605860155663429217
2^11445064+40291 has a factor: 2576034267578449
2^11462296+40291 has a factor: 23280757735312463077
2^11507800+40291 has a factor: 9829738639903373
2^11523832+40291 has a factor: 2234982526961736553
2^11551960+40291 has a factor: 2513198403336713
2^11555704+40291 has a factor: 10302066497230789
2^11576344+40291 has a factor: 489501786434752447
2^11576632+40291 has a factor: 2181355124480423
2^11576920+40291 has a factor: 1253661577718474713
2^11609944+40291 has a factor: 8439777164983837
2^11611096+40291 has a factor: 6928568057420533
2^11618536+40291 has a factor: 1725616706404343
2^11624440+40291 has a factor: 1786192776798077533
2^11634808+40291 has a factor: 3233898186594857
2^11694280+40291 has a factor: 17179699962976231
2^11695672+40291 has a factor: 7262572711619698559
2^11703448+40291 has a factor: 263385326764413589
2^11713960+40291 has a factor: 5758911847688159
2^11723560+40291 has a factor: 3717354626793035887
2^11745352+40291 has a factor: 5346048921677369
2^11774152+40291 has a factor: 24152803191390193
2^11799112+40291 has a factor: 85191497923418832769
2^11837224+40291 has a factor: 3191103733441201
2^11870824+40291 has a factor: 6890947217654977
2^11920360+40291 has a factor: 1692465902986423
2^11927320+40291 has a factor: 780354546195202007
2^11947192+40291 has a factor: 319051977671389601
2^11953192+40291 has a factor: 254496198274610839
2^11959960+40291 has a factor: 79763784720595121
2^11990488+40291 has a factor: 1232854148467715401


e

[philmoore]

Originally Posted by engracio

Completed 11m-12m, 42 factors found.
e

Excellent haul! I hope we don't have to prp this far, but if we do, your efforts will be much appreciated!