is 2 21013 - 1
has 6326 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
Actual2671,414.073177.6119%500000000100000000000.472213.3828%1,414.545280.6081%2.9961%
PrimeNet2400.000062.5000%500100000.00003.7442%0.000063.9041%1.4041%
GPU722440.000165.9091%500100000.00001.5826%0.000166.4486%0.5395%
Difference+23+1,414.0730+11.7028%+499999500+9999990000+0.4722+11.8002%+1,414.5451+14.1595%+14.1595%

Known prime factors (3 factors, 327.8 bits, 1.55976069% known):
Remaining cofactor is not a probable-prime

P-1GHz-days
exponentfactordigitsbits*kdate foundmin B1min B2min. TFmin. P-1normal P-1
210131204770003813739687606236072786.6392866725369565839450831
3 × 19 × 317 × 105882607 × 1498398557
2014-04-2310588260714983985571.480e+90.08430.1000
210131453744507285602301217741912748132103.520345915506421168396044767980
22 × 3 × 5 × 5765258440352806600746133
2017-10-06557652584403528066007461338.252e+121.457e+142.722e+14
2101326299387905659052659946243738761951322084142137.5946257885096287786765322953347632882340
22 × 3 × 5 × 59 × 242399 × 7292786486304502390480104379
2022-01-3124239972927864863045023904801043798.212e+121.844e+173.443e+17

4 Composite Factors:
exponentprime factorscomposite factordigitsbits*
2101317514277755866782075127734209550691048439202753033
91043967
58190.158
2101331684713667399876288686814656540415971887832375043
403756708268993487
68224.233
2101338232590712825247725694866138351597301687322579677
75181020343554285031521
73241.114
2101346061478458899622263992646564252531303139448680495
7678616645815979948100529194528808326309611716247
99327.753
P-1 results:
 GHz-DaysworthFactor
probability
dateuseridcompidb1b2estagefactordigitsbits*spentsaved
2001-04-29T00:00:00ANONYMOUSv4_computers10000010000000---0.000--1.842%
2001-08-18T00:00:00Alex Kruppav4_computers1000000100000000---0.003--4.560%
2002-04-28T00:00:00ANONYMOUSv4_computers163841638400---4.86067e-5--0.604%
2002-06-09T00:00:00ANONYMOUSv4_computers327683276800---9.72135e-5--0.981%
2002-07-20T00:00:00ANONYMOUSv4_computers655366553600---0.000--1.478%
2003-02-02T00:00:00ANONYMOUSv4_computers13107213107200---0.000--2.099%
2003-03-27T00:00:00ANONYMOUSv4_computers26214426214400---0.001--2.837%
2003-04-03T00:00:00ANONYMOUSv4_computers52428852428800---0.002--3.683%
2003-04-27T00:00:00ANONYMOUSv4_computers1048576104857600---0.003--4.628%
2003-05-19T00:00:00ANONYMOUSv4_computers2097152209715200---0.006--5.665%
2003-07-06T00:00:00ANONYMOUSv4_computers4194304419430400---0.012--6.787%
2003-09-29T00:00:00ANONYMOUSv4_computers8388608838860800---0.025--7.989%
2003-09-29T00:00:00ANONYMOUSv4_computers167772161677721600---0.050--9.256%
2016-11-19T00:49:55kkmrkkblmbrbkManual testing5000000001000000000012-
skipped known factor: 120477000381373968760623607
--0.472--13.383%


Trial Factoring results:
 BitsFactorGHz-Daysworth
dateuseridcompidfromtofactorbits*digitsspentsaved
2003-11-28T00:00:00eteov4_computers??86.63927734,660,2931.39205e-51.52091e+9
1999-10-15T00:00:00ANONYMOUSv4_computers252253--0.029--
2000-03-01T00:00:00ANONYMOUSv4_computers253254--0.057--
2000-08-31T00:00:00ANONYMOUSv4_computers21256--0.457--
2002-11-02T00:00:00ANONYMOUSv4_computers21257--0.914--
2022-06-16T04:12:24LordJuliusManual testing257258--0.914--
2022-06-16T04:12:24LordJuliusManual testing258259--1.827--
2022-06-16T04:12:24LordJuliusManual testing259260--3.655--
2022-06-15T12:07:01LordJuliusWhitebox_TF259260--3.655--


ECM factoring results:

Old Calculation Method

Total ECM effort:100.100 GHz-days
Estimated T-Level:39.361
DigitsB1CurvesCompleteFacMiss
20110006008 / 10060.0800.000%
25500006008 / 28021.4570.000%
302500005878 / 6409.1840.010%
3510000005423 / 15663.4633.130%
4030000004002 / 45880.87241.796%

New Calculation Method

Total ECM effort:100.100 GHz-days
Estimated T-Level:39.361
DigitsB1CompleteFacMiss
20110001,092.6970.000%
2550000282.2050.000%
3025000053.1080.000%
3510000008.1900.028%
4030000001.04635.139%
45110000000.11589.126%
50440000000.01198.895%


ECM Summary

B1B2factorcurvesGHz-days
5000050000001300.043
250000250000004550.759
10000001000000009926.623
10000001000000004292.864
30000003000000004008.012
30000004135025263808.548
30000004153442313808.564
30000004165761223808.574
30000004184301293808.589
30000004190497741,14025.78
30000004190916263808.594
30000004196702473808.599
30000005280000001824.547


Lucas-Lehmer results:
No L-L results for M21013


PRP results:
dateuseridcompidcofactorsres64PRP
2017-09-21T19:26:17Oliver KruseOliver-PC
120477000381373968760623607
212E564C42A1CB__no
2017-09-21T20:26:58Oliver KruseManual testing
120477000381373968760623607
212E564C42A1CB__no
2017-10-07T01:10:10Oliver KruseGTX-0
120477000381373968760623607
14537445072856023012177419127481
52BAD031B5AEB4C7no
2017-10-15T17:17:56YarBerManual testing
120477000381373968760623607
14537445072856023012177419127481
no
2017-10-16T13:19:20Oliver KruseThreadripper
120477000381373968760623607
14537445072856023012177419127481
52BAD031B5AEB4__no
2020-04-17T13:48:58Oliver KruseManual testing
120477000381373968760623607
14537445072856023012177419127481
9CE865A7FCF442__no
2022-01-31T10:19:12fbaurManual testing
120477000381373968760623607
14537445072856023012177419127481
262993879056590526599462437387619513220841
9CE865A7FCF442E0no
2022-02-01T05:35:19LordJuliussurface7
120477000381373968760623607
14537445072856023012177419127481
262993879056590526599462437387619513220841
9CE865A7FCF442E0no


P-1 factor-bounds graph:
B1 = 500000000, B2 = 10000000000 (P-1 stage 2)
B1 = 500000000 (P-1 stage 1)
B1 = 16777216, B2 = 1677721600 (P-1 stage 2)
B1 = 8388608, B2 = 838860800 (P-1 stage 2)
B1 = 4194304, B2 = 419430400 (P-1 stage 2)
B1 = 16777216 (P-1 stage 1)
B1 = 2097152, B2 = 209715200 (P-1 stage 2)
B1 = 8388608 (P-1 stage 1)
B1 = 1048576, B2 = 104857600 (P-1 stage 2)
B1 = 1000000, B2 = 100000000 (P-1 stage 2)
B1 = 4194304 (P-1 stage 1)
B1 = 524288, B2 = 52428800 (P-1 stage 2)
B1 = 2097152 (P-1 stage 1)
B1 = 262144, B2 = 26214400 (P-1 stage 2)
B1 = 1048576 (P-1 stage 1)
B1 = 1000000 (P-1 stage 1)
B1 = 131072, B2 = 13107200 (P-1 stage 2)
B1 = 100000, B2 = 10000000 (P-1 stage 2)
B1 = 524288 (P-1 stage 1)
B1 = 65536, B2 = 6553600 (P-1 stage 2)
B1 = 262144 (P-1 stage 1)
B1 = 32768, B2 = 3276800 (P-1 stage 2)
B1 = 131072 (P-1 stage 1)
B1 = 16384, B2 = 1638400 (P-1 stage 2)
B1 = 100000 (P-1 stage 1)
B1 = 65536 (P-1 stage 1)
B1 = 32768 (P-1 stage 1)
B1 = 16384 (P-1 stage 1)
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TF factor-bounds graph:
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Last modified: 2022-06-16T04:12:24+00:00