is 2 21313 - 1
has 6416 decimal digits
takes 0.000 GHz-days to do one PRP test
Last-known PrimeNet details:
Exponent is not assigned to anyone
-unknown- primality tests remaining
ResidueStatus
L-L-unknown--unknown-
PRP-unknown--unknown-

 Trial FactoringP-1 FactoringCombined
LimitGHz-daysProbabilityB1B2GHz-daysProbabilityGHz-daysProbabilityProb over default TF
Actual2671,394.168777.6119%500000000100000000000.472213.3953%1,394.640980.6109%2.9989%
PrimeNet2400.000062.5000%500100000.00003.7580%0.000063.9092%1.4092%
GPU722440.000165.9091%500100000.00001.5893%0.000166.4509%0.5418%
Difference+23+1,394.1686+11.7028%+499999500+9999990000+0.4722+11.8060%+1,394.6408+14.1600%+14.1600%

Known prime factors (3 factors, 186.2 bits, 0.87362620% known):
Remaining cofactor is not a probable-prime

P-1GHz-days
exponentfactordigitsbits*kdate foundmin B1min B2min. TFmin. P-1normal P-1
2131367988471826.0191595
5 × 11 × 29
-11295.643e-105.559e-91.039e-8
21313136544292071133.669320331
3 × 11 × 17 × 571
2008-08-26175717.172e-82.189e-82.716e-8
2131312102017933349217791014943227140052404739126.5092839116486029469758132347212297671
7 × 127 × 971767 × 3286391538226151486241017
2021-10-1597176732863915382261514862410179.003e+128.308e+131.552e+14

4 Composite Factors:
exponentprime factorscomposite factordigitsbits*
213139283437641616724971859.687
21313822797695302993226657103528165057865855426213746152.527
21313165246147132761338736238462974107966634246264072949160.177
2131311234832882197477428589925388999713240381419731778
7035359
57186.196
P-1 results:
 GHz-DaysworthFactor
probability
dateuseridcompidb1b2estagefactordigitsbits*spentsaved
2016-11-19T00:49:55kkmrkkblmbrbkManual testing5000000001000000000012-
skipped known factor: 67988471
skipped known factor: 13654429207
--0.472--13.395%


Trial Factoring results:
 BitsFactorGHz-Daysworth
dateuseridcompidfromtofactorbits*digitsspentsaved
2008-08-26T19:59:00ANONYMOUSManual testing??33.669111.80251e-82.08777e-55.51780e-8


ECM factoring results:

Old Calculation Method

Total ECM effort:18.300 GHz-days
Estimated T-Level:35.426
DigitsB1CurvesCompleteFacMiss
20110002651 / 10026.5100.000%
25500002651 / 2809.4680.008%
302500002621 / 6404.0951.660%
3510000001712 / 15801.08433.828%
403000000400 / 47000.08591.841%

New Calculation Method

Total ECM effort:18.300 GHz-days
Estimated T-Level:35.426
DigitsB1CompleteFacMiss
2011000344.1460.000%
255000067.5730.000%
3025000010.7220.002%
3510000001.39224.866%
4030000000.15285.862%
45110000000.01598.543%
50440000000.00199.875%


ECM Summary

B1B2factorcurvesGHz-days
500005000000300.010
250000250000009091.517
10000001000000001,3128.760
30000003000000003707.411
3000000300000000300.601


Lucas-Lehmer results:
No L-L results for M21313


PRP results:
dateuseridcompidcofactorsres64PRP
2017-09-21T19:26:49Oliver KrusePRP
67988471
13654429207
C643EB452F0A3A__no
2017-09-21T21:28:44Oliver KruseManual testing
67988471
13654429207
C643EB452F0A3A__no
2017-10-12T16:29:44kkmrkkblmbrbkManual testing
67988471
13654429207
C643EB452F0A3A__no
2020-04-17T13:49:01Oliver KruseManual testing
67988471
13654429207
F19372E6A694FF__no
2021-10-15T21:32:50SRJ2877LTOS
67988471
13654429207
121020179333492177910149432271400524047
F19372E6A694FF96no


P-1 factor-bounds graph:
B1 = 500000000, B2 = 10000000000 (P-1 stage 2)
B1 = 500000000 (P-1 stage 1)
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TF factor-bounds graph:
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Last modified: 2021-10-18T20:58:54+00:00