is 2 13691 - 1
has 4122 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-L504A105B03C3B410double-checked
PRP-unknown--unknown-

 Trial FactoringP-1 FactoringCombined
LimitGHz-daysProbabilityB1B2GHz-daysProbabilityGHz-daysProbability
Actual2672,170.324979.1045%1000000000000140013887388002628021,815,211.901645.7429%21,817,382.226588.6627%
Target2440.000268.1818%500500000.00001.3911%0.000268.6244%
Difference+23+2,170.3247+10.9227%+999999999500+1400138873879976280+21,815,211.9016+44.3519%+21,817,382.2263+20.0383%

Known prime factors:
No known factors for M13691

P-1 results:
 GHz-DaysworthFactor
probability
dateuseridcompidb1b2estagefactordigitsbits*spentsaved
2001-04-29ANONYMOUSv4_computers10000010000000---0.000--1.719%
2001-07-17Alex Kruppav4_computers1000000100000000---0.002--4.337%
2001-09-30ANONYMOUSv4_computers430000004290000000---0.078--10.680%
2002-04-28ANONYMOUSv4_computers163841638400---2.99573e-5--0.551%
2002-06-09ANONYMOUSv4_computers327683276800---5.99146e-5--0.904%
2002-07-14ANONYMOUSv4_computers655366553600---0.000--1.373%
2003-02-02ANONYMOUSv4_computers13107213107200---0.000--1.964%
2003-03-27ANONYMOUSv4_computers26214426214400---0.000--2.672%
2003-04-03ANONYMOUSv4_computers52428852428800---0.001--3.487%
2003-04-27ANONYMOUSv4_computers1048576104857600---0.002--4.402%
2003-05-19ANONYMOUSv4_computers2097152209715200---0.004--5.409%
2003-07-06ANONYMOUSv4_computers4194304419430400---0.008--6.501%
2003-09-29ANONYMOUSv4_computers8388608838860800---0.015--7.674%
2003-09-29ANONYMOUSv4_computers167772161677721600---0.031--8.916%
2011-05-13Jocelyn LaroucheManual testing400000000400000000---0.114--7.824%
2012-10-12Jocelyn LaroucheManual testing647218247647218247---0.185--8.561%
2013-02-26bcp19Toshiba-740Q10000000000100000000000---4.262--17.416%
2018-05-06James Hintz3_1_201824470561754183529213155012---35.21--22.751%
2022-03-21-Anonymous-T5810100000000000100013732677278420---1,558,297--40.444%
2022-11-20-Anonymous-T581010000000000001400138873880026280---21,815,212--45.743%


P+1 Factoring results:
dateuseridcompidb1b2startfactorSmoothdigitsbits*ghz-days
2021-05-09ATH5960X100000000024100000000027--4.099
2023-07-09masserManual testing5700000002280000000015137--0.587
2023-08-25masserManual testing57000000010203000000065--1.797


Trial Factoring results:
 BitsFactorGHz-Daysworth
dateuseridcompidfromtofactorbits*digitsspentsaved
1999-09-14ANONYMOUSv4_computers252253--0.044--
2000-01-25ANONYMOUSv4_computers253254--0.088--
2000-09-15ANONYMOUSv4_computers21256--0.701--
2002-08-24ANONYMOUSv4_computers21257--1.402--
2016-02-23LaurVManual testing257258--1.402--
2010-07-04George WoltmanManual testing258259--2.805--
2010-07-04George WoltmanManual testing259260--5.609--
2012-11-22bcp19Manual testing260261--11.22--
2015-08-27snme2pm1G1261262--22.44--
2016-09-23Sid & AndyWoody262263--71.70--
2018-10-06snme2pm1G4263264--143.4--
2018-12-03Anton RepkoManual testing263265--416.3--
2021-11-07Ruslan BorisovManual testing265266--545.8--


ECM factoring results:
Total ECM effort:360,265.782 GHz-days
Estimated T-Level:51.403
DigitsB1CompleteFacMiss
20110005,612.7690.000%
25500002,270.9120.000%
30250000723.7510.000%
351000000192.4880.000%
40300000044.0290.000%
45110000008.9660.013%
50440000001.65619.086%
551100000000.28175.537%
602600000000.04495.689%
658000000000.00699.371%


ECM Summary

B1B2factorcurvesGHz-days
5000050000002800.058
10000001000000001,9508.024
30000003000000001001.235
1100000011000000008,192370.8
430000002404906604262,7249,094
4400000044000000001,161210.2
11000000090137251153952,500302,396
260000000851710200841542048,185


Lucas-Lehmer results:
dateuseridcompidres64spent (GHz-days)
1997-01-01George Woltman504A105B03C3B4102.70017e-6
2015-04-11MadPooManual testing504A105B03C3B4102.70017e-6


PRP results:
No PRP results for M13691


P-1 factor-bounds graph:
B1 = 1000000000000, B2 = 1400138873880026280 (P-1 stage 2)
B1 = 100000000000, B2 = 100013732677278420 (P-1 stage 2)
B1 = 1000000000000 (P-1 stage 1)
B1 = 24470561754, B2 = 1835292131550 (P-1 stage 2)
B1 = 100000000000 (P-1 stage 1)
B1 = 24470561754 (P-1 stage 1)
B1 = 10000000000, B2 = 100000000000 (P-1 stage 2)
B1 = 10000000000 (P-1 stage 1)
B1 = 647218247 (P-1 stage 1)
B1 = 400000000 (P-1 stage 1)
B1 = 43000000, B2 = 4290000000 (P-1 stage 2)
B1 = 16777216, B2 = 1677721600 (P-1 stage 2)
B1 = 8388608, B2 = 838860800 (P-1 stage 2)
B1 = 43000000 (P-1 stage 1)
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=51.4 ~= 154-bit
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Last modified: 2023-10-02T12:12:48+00:00