is 2 56167 - 1
has 16908 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
Actual267529.028076.1194 %62000000077248347649473072,384.855830.8147 %72,913.883883.4781 %
Target2440.000063.6364 %500500000.00002.1090 %0.000064.4033 %
Difference+23+529.0280+12.4830 %+619999500+772483476444730+72,384.8557+28.7057%+72,913.8837+19.0749 %

Known prime factors (3 factors, 137.1 bits, 0.24405654% known):
Remaining cofactor is not a probable-prime

P-1GHz-days
exponentfactordigitsbits*kdate foundmin B1min B2min. TFmin. P-1normal P-1
561674942697722.23744
22 × 11
-4119.948e-127.535e-91.400e-8
561676119400266711239.1555447505
3 × 5 × 7 × 29 × 1789
2008-08-262917891.304e-62.148e-73.124e-7
56167608539327480443225988392375.688541723189310843757
3 × 7 × 863 × 152381 × 196162739
2010-05-01152381196162739136,2350.01860.0343

4 Composite Factors:
P-1 results:
dateusercompB1B2BSstagefactordigitsbits*GHz-daysFac Prob
2016-10-02kkmrkkblmbrbkManual testing100000000200000000012
skipped known factor: 4942697
skipped known factor: 611940026671
skipped known factor: 60853932748044322598839
---39.708%
2023-04-23JacobZGreatLakes620000000772483476494730
skipped known factor: 4942697
skipped known factor: 611940026671
skipped known factor: 60853932748044322598839
--113,57870.942%


P+1 Factoring results:
dateuseridcompidb1b2startfactorSmoothdigitsbits*ghz-days
2021-05-03ATHcolab-Pp215000000150000000027--0.176


Trial Factoring results:
5758596061626364656667
 BitsFactor
dateuseridcompidfromtofactorbits*digitsGHz-days
2008-08-26ANONYMOUSManual testing??
39.155
12


ECM factoring results:
Total ECM effort:112.824 GHz-days
Estimated T-Level:33.217
DigitsB1CompleteFacMiss
2011000175.2400.000%
255000033.3580.000%
302500005.0370.649%
3510000000.64352.548%
4030000000.07093.207%
45110000000.00799.328%


ECM Summary

B1B2factorcurvesGHz-days
10.006
5000050000002760.321
250000250000005843.613
100000010000000044812.40
1000000312500000010.268
1000000312500000010.268
213444257891383555025.08
246049266161195105028.68
300000099242243105042.45


Lucas-Lehmer results:
No L-L results for M56167


PRP results:
dateuseridcompidcofactorsres64
2017-09-21Oliver KruseOllaptop
4942697
611940026671
60853932748044322598839
6508C352EA4D2F1A
2017-09-21Oliver KruseManual testing
4942697
611940026671
60853932748044322598839
6508C352EA4D2F1A
2017-10-02kkmrkkblmbrbkManual testing
4942697
611940026671
60853932748044322598839
6508C352EA4D2F1A
2017-12-07ATHxps
4942697
611940026671
60853932748044322598839
6508C352EA4D2F1A
2020-04-17Oliver KruseAddPrpType5
4942697
611940026671
60853932748044322598839
ACAC9624B6D6D647
2024-02-03Wentao HuangManual testing
4942697
611940026671
60853932748044322598839
ACAC9624B6D6D647


CERT results:
No CERT results for M56167


P-1 factor-bounds graph:
B1 = 620000000, B2 = 772483476494730 (P-1 stage 2)
B1 = 620000000 (P-1 stage 1)
B1 = 100000000, B2 = 2000000000 (P-1 stage 2)
B1 = 100000000 (P-1 stage 1)
100
101
102
103
104
105
106
107
108
109
100
101
102
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
ECM T-Level=33.22 ~= 94-bit
250
260
270
280
290
2100
JSON version of this page
Last modified: 2024-03-03T02:29:32+00:00