is 2 41281 - 1
has 12427 decimal digits
takes 0.000 GHz-days to do one PRP test
Last-known PrimeNet details:
Exponent is not assigned to anyone
0 primality tests remaining
ResidueStatus
L-L-unknown--unknown-
PRP-unknown--unknown-

 Trial FactoringP-1 FactoringCombined
LimitGHz-daysProbabilityB1B2GHz-daysProbabilityGHz-daysProbability
Actualunknown88000000078936726129261044,518.982170.6421%44,518.982170.6421%
Target2440.000163.6364%500500000.00001.9303%0.000164.3383%
Difference-44-0.0001-63.6364%+879999500+789367261242610+44,518.9821+68.7119%+44,518.9821+6.3039%

Known prime factors (2 factors, 154.0 bits, 0.37301059% known):
Remaining cofactor is not a probable-prime

P-1GHz-days
exponentfactordigitsbits*kdate foundmin B1min B2min. TFmin. P-1normal P-1
4128151531476217332586886572272.12662415489229103688
23 × 3 × 17 × 7207 × 10667 × 1989919
2014-04-2310667198991938,1520.00010.0002
4128143780324316889415817469292581.85753027209027021409144
23 × 31 × 577 × 53269 × 6956595181
2009-04-2253269695659518119,679,9050.39240.7328

1 Composite Factors:
P-1 results:
 GHz-DaysworthFactor
probability
dateuseridcompidb1b2estagefactordigitsbits*spentsaved
2016-09-13kkmrkkblmbrbkManual testing100000000200000000012-
skipped known factor: 5153147621733258688657
--0.211--39.141%
2021-12-21Lisander ViaeneManual testing10000000001000000000-
skipped known factor: 5153147621733258688657
--1.035--34.679%
2023-04-08JacobZMServer880000000789367261292610-
skipped known factor: 5153147621733258688657
skipped known factor: 4378032431688941581746929
--44,519--70.642%


P+1 Factoring results:
dateuseridcompidb1b2startfactorSmoothdigitsbits*ghz-days
2021-04-27gLausslaptop-klaus10000000100000000027--0.071


Trial Factoring results:
No TF results for M41281


ECM factoring results:
Total ECM effort:56.558 GHz-days
Estimated T-Level:35.676
DigitsB1CompleteFacMiss
2011000357.7950.000%
255000068.9330.000%
3025000010.4770.003%
3510000001.30227.191%
4030000000.13587.346%
45110000000.01298.807%


ECM Summary

B1B2factorcurvesGHz-days
10.00000e+0
5000050000002590.193
250000250000005832.171
10000001000000001,66924.86
3000000114863248505029.33


Lucas-Lehmer results:
No L-L results for M41281


PRP results:
dateuseridcompidcofactorsres64PRP
2017-09-21Oliver KruseOliver-PC69CEA30684A3CA__?
2017-09-21Oliver KruseManual testing69CEA30684A3CA__?
2017-10-02kkmrkkblmbrbkManual testing
5153147621733258688657
4378032431688941581746929
69CEA30684A3CA__no
2017-12-07ATHxps
5153147621733258688657
4378032431688941581746929
69CEA30684A3CA__no
2020-04-17Oliver KruseManual testing
5153147621733258688657
4378032431688941581746929
4DA3AB41E1DDEF__no


P-1 factor-bounds graph:
B1 = 880000000, B2 = 789367261292610 (P-1 stage 2)
B1 = 1000000000 (P-1 stage 1)
B1 = 880000000 (P-1 stage 1)
B1 = 100000000, B2 = 2000000000 (P-1 stage 2)
B1 = 100000000 (P-1 stage 1)
103
104
105
106
107
108
109
103
104
105
106
107
108
109
1010
1011
1012
1013
1014
1015
TF factor-bounds graph:
this exponent TF target: 44
TF double-checked to: 67.9
ECM T-Level=35.68 ~= 102-bit
250
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2100
2110
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Last modified: 2023-10-02T12:12:48+00:00