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Old 2019-12-18, 15:18   #31
kriesel
 
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"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

13·373 Posts
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.

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 selftest for each combination in use at least annually, at installation, and upon change of configuration. Following are some candidates for such self-test.

Note, the larger ones can take several days, even on a Radeon VII.

Exponents, bounds required, etc.
Code:
Exponent      Min B1       Min B2     fft length         notes
4444091            7         2,557     256k
10000831      29,173       492,251    ?
24000577           1       281,339    ?
50001781      94,709     4,067,587    2688k
51558151       5,953     2,034,041    2880k
54447193       1,181       682,009    3072k
58610467      70,843       694,201    3200k
61012769      10,273     1,572,097    3360k    
81229789       6,709    11,282,221    4704K    
100000081      1,289     7,554,653    5600K  
110505011    114,967     8,616,197    6144K
120002191      1,563     3,109,391    7168K    
150000713     15,131     2,294,519    8640K    
200000183        953     1,138,061   11200K        
200001187    204,983       207,821   11200K    
200003173      4,651       229,813   11200K  
230086243    321,547       417,541   ?
249500221          4    2.58951e+9   14336K    
249500501        307       167,381   14336K    
290001377      2,551    34,354,769   16384K    takes days
301000159      1,499     8,999,819   18432K
332230189    343,289     5,552,263   18816K
353466917     27,299     7,831,403   ?
407363239    508,103    10,407,589   23040K
423000089      9,221    73,375,433   24192K
464000021      3,229    63,576,391   ?
502000027     13,777     1,099,081   28672K
563021377     105253   14013184573   ?
654036583        101    9507343133   ?
745964951       2617          7963   ?
901000031  1,362,211    22,449,467   51840K
940216091     269393    6481528541   ?
CUDAPm1 format worktodo lines:
Code:
PFactor=1,2,4444091,-1,70,2
PFactor=1,2,10000831,-1,68,2
PFactor=1,2,24000577,-1,70,2
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=1,2,301000159,-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=1,2,502000027,-1,82,2
PFactor=1,2,563021377,-1,81,2
PFactor=1,2,654036583,-1,84,2
PFactor=1,2,745964951,-1,84,2
PFactor=1,2,901000031,-1,85,2
PFactor=1,2,940216091,-1,85,2
Factors that should be found:
Code:
Exponent    Factor (may be composite)    Prime factors
 4444091    1809798096458971047321927127  = 8888183 * 319974553 * 636358278473
10000831    646560662529991467527
24000577    13504596665207
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
301000159   99812588622057998165480647
332230189   400336212296331535712337247
353466917   32645162170211204627569
407363239   2460083406159745463265647
423000089   7999281314567748179722151
464000021   56208073342032516397974073
502000027   2107472748472812989445447752584121
563021377   4982501757616947169867879
654036583   45218388371594348767609
745964951   87913098632237818693849
901000031   266276073654639633298220609
940216091   3283382049964706665517567
(We need more coverage of the mersenne.org 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 2021-01-08 at 05:49 Reason: added links to mersenne.ca exponent pages; correct 50001781 factor
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