is 2 56113 - 1
has 16892 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
Actual267529.537176.1194%62000000077248347649473072,384.855830.8135%72,914.392983.4778%
Target2440.000063.6364%500500000.00002.1084%0.000064.4031%
Difference+23+529.5371+12.4830%+619999500+772483476444730+72,384.8557+28.7050%+72,914.3928+19.0748%

Known prime factors (4 factors, 298.8 bits, 0.53251897% known):
Remaining cofactor is not a probable-prime

P-1GHz-days
exponentfactordigitsbits*kdate foundmin B1min B2min. TFmin. P-1normal P-1
561139062357322251771549.6878075096076
22 × 3 × 43 × 2243 × 6977
-224369770.00174.301e-67.851e-6
5611321822653373190311650.95519445274155
5 × 29 × 5449 × 24611
2008-08-265449246110.00481.117e-51.907e-5
56113891019886370169671756.306793951389491
13 × 941 × 64902427
2009-06-20941649024270.18930.00610.0114
56113507515930684105200009561326689602113458389743141.86445222669495848127885655848617040802796
22 × 61 × 22441 × 1018019 × 5259929 × 156797717 × 9836682697
2023-04-2315679771798366826972.569e+121.17671.7215

11 Composite Factors:
P-1 results:
 GHz-DaysworthFactor
probability
dateuseridcompidb1b2estagefactordigitsbits*spentsaved
2016-10-02kkmrkkblmbrbkManual testing100000000200000000012-
skipped known factor: 906235732225177
skipped known factor: 2182265337319031
skipped known factor: 89101988637016967
--0.350--11.231%
2023-04-23JacobZGreatLakes62000000077248347649473043141.86472,3850.000144,77030.813%


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


Trial Factoring results:
 BitsFactorGHz-Daysworth
dateuseridcompidfromtofactorbits*digitsspentsaved
2008-08-26ANONYMOUSManual testing??50.955160.0020.0000.004


ECM factoring results:
Total ECM effort:29.657 GHz-days
Estimated T-Level:32.134
DigitsB1CompleteFacMiss
2011000149.5550.000%
255000026.8850.000%
302500003.7382.381%
3510000000.42765.263%
4030000000.04195.989%
45110000000.00399.666%


ECM Summary

B1B2factorcurvesGHz-days
10.00000e+0
5000050000002790.345
250000250000005843.613
100000010000000045211.19
1000000324317565020.556
100000032599545015013.96


Lucas-Lehmer results:
No L-L results for M56113


PRP results:
dateuseridcompidcofactorsres64PRP
2017-09-21Oliver KrusePRP
906235732225177
2182265337319031
89101988637016967
BC3098DC9488DB40no
2017-09-21Oliver KruseManual testing
906235732225177
2182265337319031
89101988637016967
BC3098DC9488DB40no
2017-10-02kkmrkkblmbrbkManual testing
906235732225177
2182265337319031
89101988637016967
BC3098DC9488DB__no
2017-12-07ATHxps
906235732225177
2182265337319031
89101988637016967
BC3098DC9488DB__no
2020-04-17Oliver KruseAddPrpType5
906235732225177
2182265337319031
89101988637016967
A3CE3A758A8447__no
2023-04-23JacobZGreatLakes
906235732225177
2182265337319031
89101988637016967
5075159306841052000095613266896021134583897
A3CE3A758A8447DBno


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)
101
102
103
104
105
106
107
108
109
101
102
103
104
105
106
107
108
109
1010
1011
1012
1013
1014
1015
TF factor-bounds graph:
2
this exponent TF target: 44
TF double-checked to: 67.9
ECM T-Level=32.13 ~= 90-bit
250
260
270
280
290
2100
2110
2120
2130
2140
2150
Last modified: 2023-09-25T11:53:03+00:00