"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
22·7·269 Posts
|
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
|