is 2 41411 - 1
has 12466 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-L5539AAAF8088442Bdouble-checked
PRP-unknown--unknown-

 Trial FactoringP-1 FactoringCombined
LimitGHz-daysProbabilityB1B2GHz-daysProbabilityGHz-daysProbability
Actual267717.536876.1194%500000000050028619899258028,219.645631.9805%28,937.182583.7565%
Target2440.000163.6364%500500000.00001.9320%0.000164.3389%
Difference+23+717.5368+12.4830%+4999999500+500286198942580+28,219.6456+30.0484%+28,937.1824+19.4176%

Known prime factors:
No known factors for M41411

P-1 results:
 GHz-DaysworthFactor
probability
dateuseridcompidb1b2estagefactordigitsbits*spentsaved
2001-04-29ANONYMOUSv4_computers10000010000000---0.001--2.053%
2001-08-18Alex Kruppav4_computers1000000100000000---0.007--4.934%
2002-04-28ANONYMOUSv4_computers163841638400---0.000--0.697%
2002-06-09ANONYMOUSv4_computers327683276800---0.000--1.115%
2002-07-20ANONYMOUSv4_computers655366553600---0.000--1.659%
2003-02-02ANONYMOUSv4_computers13107213107200---0.001--2.329%
2003-03-27ANONYMOUSv4_computers26214426214400---0.002--3.117%
2003-04-03ANONYMOUSv4_computers52428852428800---0.003--4.012%
2003-04-27ANONYMOUSv4_computers1048576104857600---0.007--5.005%
2003-05-26ANONYMOUSv4_computers2097152209715200---0.014--6.091%
2003-07-21ANONYMOUSv4_computers4194304419430400---0.028--7.261%
2003-10-08ANONYMOUSv4_computers8388608838860800---0.056--8.508%
2003-10-14ANONYMOUSv4_computers167772161677721600---0.111--9.812%
2012-05-29Jocelyn LaroucheManual testing6188694061886940---0.064--5.798%
2012-06-15alpertronManual testing1000000002000000000---0.211--10.978%
2016-05-09Jocelyn LaroucheManual testing200000000360000000012---0.399--12.097%
2019-03-21alexManual testing10000000005000000000012---3.799--16.840%
2022-05-16ATHManual testing5000000000500286198992580---28,220--31.980%


P+1 Factoring results:
dateuseridcompidb1b2startfactorSmoothdigitsbits*ghz-days
2021-04-27gLausslaptop-klaus10000000100000000027--0.071
2021-05-06GURA LOVE10000000400000000065--0.236
2023-07-04masserManual testing170000000680000000012713--0.634
2023-08-15masserManual testing1700000003043000000065--1.940


Trial Factoring results:
 BitsFactorGHz-Daysworth
dateuseridcompidfromtofactorbits*digitsspentsaved
1999-10-21ANONYMOUSv4_computers252253--0.014--
2000-03-22ANONYMOUSv4_computers253254--0.029--
2000-09-08ANONYMOUSv4_computers21256--0.232--
2002-11-16ANONYMOUSv4_computers21257--0.464--
2016-02-23LaurVManual testing257258--0.464--
2009-01-06Sturle Sundeherrick.ifi258259--0.927--
2009-01-11Sturle Sundehaydn.ifi259260--1.854--
2013-11-27LaurVManual testing260261--3.709--
2014-06-28Sid & AndyMrs_Potato_Head261262--7.418--
2016-10-08Sid & AndyBullseye262263--23.71--
2018-07-29YxinityYGSMainFrame263264--47.41--
2018-07-30YxinityManual testing263264--47.41--
2019-10-05YxinityYGSMainFrame264265--90.23--
2019-10-07YxinityManual testing264265--90.23--
2021-05-30Ruslan BorisovManual testing265266--180.5--


ECM factoring results:
Total ECM effort:8,770.367 GHz-days
Estimated T-Level:45.940
DigitsB1CompleteFacMiss
20110004,048.7330.000%
25500001,170.0940.000%
30250000292.0750.000%
35100000058.4610.000%
4030000009.9070.005%
45110000001.45423.371%
50440000000.18882.857%
551100000000.02297.834%
602600000000.00299.778%


ECM Summary

B1B2factorcurvesGHz-days
100000010000000010.015
30000003000000004,972222.2
1100000011000000001,750286.7
11000000202400000035073.02
11000000315186771905,0008,188


Lucas-Lehmer results:
dateuseridcompidres64spent (GHz-days)
1997-01-01George Woltman5539AAAF8088442B2.95629e-5
2015-04-11MadPooManual testing5539AAAF8088442B2.95629e-5


PRP results:
No PRP results for M41411


P-1 factor-bounds graph:
B1 = 5000000000, B2 = 500286198992580 (P-1 stage 2)
B1 = 5000000000 (P-1 stage 1)
B1 = 1000000000, B2 = 50000000000 (P-1 stage 2)
B1 = 1000000000 (P-1 stage 1)
B1 = 200000000, B2 = 3600000000 (P-1 stage 2)
B1 = 100000000, B2 = 2000000000 (P-1 stage 2)
B1 = 200000000 (P-1 stage 1)
B1 = 16777216, B2 = 1677721600 (P-1 stage 2)
B1 = 100000000 (P-1 stage 1)
B1 = 61886940 (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: 67.9
ECM T-Level=45.94 ~= 136-bit
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Last modified: 2023-10-02T12:12:48+00:00