is 2 21317 - 1
has 6418 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-L48604C2FF85BEC29double-checked
PRP-unknown--unknown-

 Trial FactoringP-1 FactoringCombined
LimitGHz-daysProbabilityB1B2GHz-daysProbabilityGHz-daysProbability
Actual2671,393.907177.6119%4000000000016387889450983050414,303.394137.7780%415,697.301286.0697%
Target2440.000165.9091%500100000.00001.5894%0.000166.4509%
Difference+23+1,393.9070+11.7028%+39999999500+16387889450973050+414,303.3941+36.1886%+415,697.3011+19.6188%

Known prime factors:
No known factors for M21317

P-1 results:
 GHz-DaysworthFactor
probability
dateuseridcompidb1b2estagefactordigitsbits*spentsaved
2001-04-29ANONYMOUSv4_computers10000010000000---0.000--1.847%
2001-08-18Alex Kruppav4_computers1000000100000000---0.003--4.568%
2002-04-28ANONYMOUSv4_computers163841638400---4.86067e-5--0.606%
2002-06-09ANONYMOUSv4_computers327683276800---9.72135e-5--0.984%
2002-07-20ANONYMOUSv4_computers655366553600---0.000--1.482%
2003-02-02ANONYMOUSv4_computers13107213107200---0.000--2.104%
2003-03-27ANONYMOUSv4_computers26214426214400---0.001--2.843%
2003-04-03ANONYMOUSv4_computers52428852428800---0.002--3.690%
2003-04-27ANONYMOUSv4_computers1048576104857600---0.003--4.636%
2003-05-19ANONYMOUSv4_computers2097152209715200---0.006--5.674%
2003-07-06ANONYMOUSv4_computers4194304419430400---0.012--6.797%
2003-09-29ANONYMOUSv4_computers8388608838860800---0.025--7.999%
2003-09-29ANONYMOUSv4_computers167772161677721600---0.050--9.268%
2006-02-15Jocelyn Larouchev4_computers100000000100000000---0.046--6.084%
2013-03-10bcp19Toshiba-740Q10000000000100000000000---6.915--17.831%
2021-08-29Seth_TrManual testing3000000000030000000000---13.92--15.324%
2021-09-11Seth_TrManual testing300000000003000000000000---89.00--24.125%
2022-05-30ATHManual testing4000000000016387889450983050---414,303--37.778%


P+1 Factoring results:
dateuseridcompidb1b2startfactorSmoothdigitsbits*ghz-days
2021-05-08ATH5960X50000000010150000000027--2.855


Trial Factoring results:
 BitsFactorGHz-Daysworth
dateuseridcompidfromtofactorbits*digitsspentsaved
1999-10-15ANONYMOUSv4_computers252253--0.028--
2000-03-01ANONYMOUSv4_computers253254--0.056--
2000-08-31ANONYMOUSv4_computers21256--0.450--
2002-11-02ANONYMOUSv4_computers21257--0.901--
2016-02-23LaurVManual testing257258--0.901--
2009-01-20Sturle Sundeeames.ifi258259--1.801--
2009-02-04Sturle Sundeniemeyer.ifi259260--3.603--
2011-12-07bcp19Main-2500k260261--7.205--
2011-12-10bcp19Main-2500k261262--14.41--
2016-10-01Sid & AndyMrs_Potato_Head262263--46.05--
2018-04-02YxinityYGSMainFrame263264--92.10--
2018-04-02YxinityManual testing263264--92.10--
2018-10-22YxinityYGSMainFrame264265--175.3--
2018-10-22YxinityManual testing264265--175.3--
2020-01-22YxinityYGSMainFrame265266--350.6--
2020-01-22YxinityManual testing265266--350.6--


ECM factoring results:
Total ECM effort:5,997.690 GHz-days
Estimated T-Level:43.757
DigitsB1CompleteFacMiss
20110001,495.2670.000%
2550000458.3290.000%
30250000116.4250.000%
35100000024.5500.000%
4030000004.5621.044%
45110000000.75147.171%
50440000000.11389.349%
551100000000.01598.467%
602600000000.00299.806%


ECM Summary

B1B2factorcurvesGHz-days
10000001000000001,0607.077
30000003000000001,27325.50
11000000110000000078857.87
11000000201955005530028.02
11000000202142116430028.04
11000000202223100930028.04
11000000202268479630028.05
11000000202280584820018.70
11000000202330899230028.05
110000003500000000010080.97
440000005127553130705005,667
various30.1494


Lucas-Lehmer results:
dateuseridcompidres64spent (GHz-days)
1997-01-01George Woltman48604C2FF85BEC296.82144e-6
2015-04-11MadPooManual testing48604C2FF85BEC296.82144e-6


PRP results:
No PRP results for M21317


P-1 factor-bounds graph:
B1 = 40000000000, B2 = 16387889450983050 (P-1 stage 2)
B1 = 30000000000, B2 = 3000000000000 (P-1 stage 2)
B1 = 40000000000 (P-1 stage 1)
B1 = 30000000000 (P-1 stage 1)
B1 = 10000000000, B2 = 100000000000 (P-1 stage 2)
B1 = 10000000000 (P-1 stage 1)
B1 = 16777216, B2 = 1677721600 (P-1 stage 2)
B1 = 100000000 (P-1 stage 1)
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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this exponent TF target: 44
TF double-checked to: 67.7
ECM T-Level=43.76 ~= 129-bit
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Last modified: 2023-03-23T17:39:31+00:00