is 2 31253 - 1
has 9409 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-LAF09E6489D46A585double-checked
PRP-unknown--unknown-

 Trial FactoringP-1 FactoringCombined
LimitGHz-daysProbabilityB1B2GHz-daysProbabilityGHz-daysProbability
Actual267950.754177.6119 %12282563792201241297629372087,581.103434.3552 %88,531.857585.3034 %
Target2440.000165.9091 %500500000.00001.7798 %0.000166.5159 %
Difference+23+950.7540+11.7028 %+12282563292+2012412976243720+87,581.1034+32.5754%+88,531.8574+18.7875 %

Known prime factors:
No known factors for M31253

P-1 results:
dateusercompB1B2BSstagefactordigitsbits*GHz-daysFac Prob
2001-04-29ANONYMOUSv4_computers10000010000000--0.00120.887%
2001-08-18Alex Kruppav4_computers1000000100000000--0.00528.981%
2002-04-28ANONYMOUSv4_computers163841638400--8.37000e-514.286%
2002-06-09ANONYMOUSv4_computers327683276800--0.00016.830%
2002-07-20ANONYMOUSv4_computers65536655360012--0.00019.358%
2003-02-02ANONYMOUSv4_computers1310721310720030--0.00121.861%
2003-03-27ANONYMOUSv4_computers2621442621440030--0.00124.330%
2003-04-03ANONYMOUSv4_computers5242885242880048--0.00326.759%
2003-04-27ANONYMOUSv4_computers104857610485760048--0.00529.143%
2003-05-19ANONYMOUSv4_computers209715220971520012--0.01131.475%
2003-07-13ANONYMOUSv4_computers419430441943040012--0.02133.754%
2003-10-08ANONYMOUSv4_computers16777216167772160012--0.08638.139%
2003-10-08ANONYMOUSv4_computers838860883886080012--0.04335.976%
2013-11-09David Campeaui5-2500k2079500001102135000012--0.63743.637%
2017-01-23mikrS067600000000048000000000012--25.4253.005%
2022-09-13One ManRyzen2600122825637922012412976293720--113,50772.856%


P+1 Factoring results:
dateuseridcompidb1b2startfactorSmoothdigitsbits*ghz-days
2021-05-07ATH5960X50000000010150000000027--4.914
2023-07-06masserManual testing23000000092000000008231--0.662
2023-08-25masserManual testing2300000004117000000065--2.025


Trial Factoring results:
5758596061626364656667
 BitsFactor
dateuseridcompidfromtofactorbits*digitsGHz-days
1999-10-29ANONYMOUSv4_computers2522530.019
2000-03-08ANONYMOUSv4_computers2532540.038
2000-09-08ANONYMOUSv4_computers212560.307
2002-12-02ANONYMOUSv4_computers212570.614
2016-02-23LaurVManual testing2572580.614
2009-01-07Sturle Sundehoffman.ifi2582591.229
2009-02-20monstkingslake2592602.457
2012-03-23bcp19Manual testing26026214.74
2016-12-09Sid & AndyWoody26226331.41
2018-06-04YxinityYGSMainFrame26326462.82
2018-06-04YxinityManual testing263264
2019-12-10YxinityYGSMainFrame264265119.6
2019-12-11YxinityManual testing264265
2020-12-25YxinityYGSMainFrame265266239.1
2020-12-28YxinityManual testing265266


ECM factoring results:
Total ECM effort:16,158.578 GHz-days
Estimated T-Level:43.377
DigitsB1CompleteFacMiss
20110001,423.3000.000%
2550000440.6510.000%
30250000106.7390.000%
35100000021.7590.000%
4030000003.9891.853%
45110000000.67550.896%
50440000000.10889.750%
551100000000.01698.367%
602600000000.00299.768%


ECM Summary

B1B2factorcurvesGHz-days
10000001000000006456.750
30000003000000003,159108.9
500000050000000060034.48
110000001100000000950120.1
11000000147400000070899.41
399132291572267812115774,550
39913229157482659362611651.0
4399217094335944703011391.7
110000000134088361407020010,196


Lucas-Lehmer results:
dateuseridcompidres64spent (GHz-days)
2015-04-11MadPooManual testingAF09E6489D46A5851.72152e-5


PRP results:
No PRP results for M31253


CERT results:
No CERT results for M31253


P-1 factor-bounds graph:
B1 = 12282563792, B2 = 2012412976293720 (P-1 stage 2)
B1 = 6000000000, B2 = 480000000000 (P-1 stage 2)
B1 = 12282563792 (P-1 stage 1)
B1 = 6000000000 (P-1 stage 1)
B1 = 207950000, B2 = 11021350000 (P-1 stage 2)
B1 = 207950000 (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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264
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253
this exponent TF target: 44
TF double-checked to: 67
ECM T-Level=43.38 ~= 127-bit
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Last modified: 2024-03-13T02:15:48+00:00