is 2 406531 - 1
has 122379 decimal digits
takes 0.004 GHz-days to do one PRP test
Last-known PrimeNet details:
Exponent is not assigned to anyone
factored, 0 LL tests remaining
ResidueStatus
L-LE362FCFA2E7A5BD5double-checked
PRP-unknown--unknown-

 Trial FactoringP-1 FactoringCombined
LimitGHz-daysProbabilityB1B2GHz-daysProbabilityGHz-daysProbability
Actual26773.091471.6418 %100000007200000000.684310.3438 %73.775774.5751 %
Target2440.000056.8182 %700011000000.000913.0916 %0.000962.4714 %
Difference+23+73.0914+14.8236 %+9993000+718900000+0.6834-2.7478 %+73.7748+12.1037 %

Known prime factors (1 factor, 113.4 bits, 0.02790260% known):
Remaining cofactor is not a probable-prime

P-1GHz-days
exponentfactordigitsbits*kdate foundmin B1min B2min. TFmin. P-1normal P-1
4065311401681424939386909400349546298655135113.43317239539234884755521723430025
52 × 18696871 × 36882191110768760231
2019-04-2318696871368821911107687602314.595e+112.825e+105.276e+10

P-1 results:
dateusercompB1B2BSstagefactordigitsbits*GHz-daysFac Prob
2002-06-15ANONYMOUSv4_computers32768327680012--0.00321.698%
2002-08-17ANONYMOUSv4_computers65536655360012--0.00624.336%
2003-03-27ANONYMOUSv4_computers1310721310720030--0.01226.924%
2006-01-15Jossv4_computers406531406531--0.00616.455%
2010-11-02ANONYMOUSManual testing50000005000000--0.07024.059%
2011-02-01Rob_Deetwopc5000000100000006--0.07426.703%
2011-02-02Rob_Deetwopc50000002000000012--0.08229.219%
2011-02-03Rob_Deetwopc50000003000000012--0.08930.636%
2011-02-04Rob_Deetwopc50000004000000012--0.09731.618%
2011-02-05Rob_Deetwopc50000005000000012--0.10532.368%
2011-02-06Rob_Deetwopc50000006000000012--0.11232.971%
2011-02-07Rob_Deetwopc50000007000000012--0.12033.476%
2011-02-08Rob_Deetwopc50000008000000012--0.12833.910%
2011-02-09Rob_Deetwopc50000009000000012--0.13534.289%
2011-02-10Rob_Deetwopc500000010000000012--0.14334.626%
2011-02-11Rob_Deetwopc500000011000000012--0.15134.929%
2011-02-12Rob_Deetwopc500000012000000012--0.15835.203%
2011-02-13Rob_Deetwopc500000013000000012--0.16635.455%
2011-02-14Rob_Deetwopc500000014000000012--0.17435.687%
2016-05-13NumberwangManual testing4545113625---11.021%
2016-05-20JossManual testing1000000018000000012--0.27136.428%
2016-06-22JossManual testing1000000036000000012--0.40938.622%
2016-09-07JossManual testing1000000072000000012--0.68440.724%


Trial Factoring results:
5758596061626364656667
 BitsFactor
dateuseridcompidfromtofactorbits*digitsGHz-days
2001-03-25ANONYMOUSv4_computers212560.024
2002-01-08ANONYMOUSv4_computers212570.047
2003-12-23ANONYMOUSv4_computers212580.094
2016-02-23Mark RoseManual testing2582600.283
2011-05-05Sid & AndyBuzz2602610.378
2015-07-14NRManual testing2612620.756
2015-11-08Gordon SpenceManual testing2622647.244
2017-12-14Gordon SpenceManual testing2642659.191
2018-11-30Gordon SpenceManual testing26526618.38


ECM factoring results:
Total ECM effort:32.392 GHz-days
Estimated T-Level:29.684
DigitsB1CompleteFacMiss
201100061.8600.000%
25500008.9120.013%
302500000.93739.185%
3510000000.07792.592%
4030000000.00599.487%


ECM Summary

B1B2factorcurvesGHz-days
5000050000002802.768
2500002500000019410.23
2500002500000036819.40


Lucas-Lehmer results:
dateuseridcompidres64spent (GHz-days)
2002-02-03ANONYMOUSv4_computersE362FCFA2E7A5BD50.004


PRP results:
dateuseridcompidcofactorsres64
2019-04-24artorollofourth
14016814249393869094003495462986551
E5DAC0D0A26D5C44
2019-04-26arnaudstm-11-010
14016814249393869094003495462986551
E5DAC0D0A26D5C44


CERT results:
No CERT results for M406531


P-1 factor-bounds graph:
B1 = 10000000, B2 = 720000000 (P-1 stage 2)
B1 = 10000000, B2 = 360000000 (P-1 stage 2)
B1 = 10000000, B2 = 180000000 (P-1 stage 2)
B1 = 5000000, B2 = 140000000 (P-1 stage 2)
B1 = 5000000, B2 = 130000000 (P-1 stage 2)
B1 = 5000000, B2 = 120000000 (P-1 stage 2)
B1 = 5000000, B2 = 110000000 (P-1 stage 2)
B1 = 5000000, B2 = 100000000 (P-1 stage 2)
B1 = 10000000 (P-1 stage 1)
B1 = 5000000, B2 = 90000000 (P-1 stage 2)
B1 = 5000000, B2 = 80000000 (P-1 stage 2)
B1 = 5000000, B2 = 70000000 (P-1 stage 2)
B1 = 5000000, B2 = 60000000 (P-1 stage 2)
B1 = 5000000, B2 = 50000000 (P-1 stage 2)
B1 = 5000000, B2 = 40000000 (P-1 stage 2)
B1 = 5000000, B2 = 30000000 (P-1 stage 2)
B1 = 5000000, B2 = 20000000 (P-1 stage 2)
B1 = 5000000, B2 = 10000000 (P-1 stage 2)
B1 = 5000000 (P-1 stage 1)
B1 = 131072, B2 = 13107200 (P-1 stage 2)
B1 = 65536, B2 = 6553600 (P-1 stage 2)
B1 = 406531 (P-1 stage 1)
B1 = 32768, B2 = 3276800 (P-1 stage 2)
B1 = 131072 (P-1 stage 1)
B1 = 65536 (P-1 stage 1)
B1 = 32768 (P-1 stage 1)
B1 = 4545, B2 = 113625 (P-1 stage 2)
B1 = 4545 (P-1 stage 1)
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TF factor-bounds graph:
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this exponent TF target: 44
TF double-checked to: 67
ECM T-Level=29.68 ~= 82-bit
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Last modified: 2024-03-13T02:15:48+00:00