is 2 9857 - 1
has 2968 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-L05646A61B1A6A75Bdouble-checked
PRP-unknown--unknown-

 Trial FactoringP-1 FactoringCombined
LimitGHz-daysProbabilityB1B2GHz-daysProbabilityGHz-daysProbability
Actual2673,014.499179.1045%60000000000480000000000056.272524.2787%3,070.771684.1776%
Target2440.000268.1818%500100000.00001.2582%0.000268.5822%
Difference+23+3,014.4989+10.9227%+59999999500+4799999990000+56.2725+23.0205%+3,070.7713+15.5955%

Known prime factors:
No known factors for M9857

P-1 results:
 GHz-DaysworthFactor
probability
dateuseridcompidb1b2estagefactordigitsbits*spentsaved
2001-02-11ANONYMOUSv4_computers1000000100000000---0.001--4.171%
2001-06-30ANONYMOUSv4_computers430000004290000000---0.049--10.404%
2001-07-07ANONYMOUSv4_computers30000000004290000000---0.543--11.437%
2002-06-23ANONYMOUSv4_computers10737418244290000000---0.221--11.490%
2002-09-07ANONYMOUSv4_computers21474836484290000000---0.400--11.475%
2002-11-09ANONYMOUSv4_computers32212254724290000000---0.580--11.426%
2003-03-16ANONYMOUSv4_computers42900000002147483647---0.759--11.372%
2015-02-11JayderHPJared135949197380210026404---1.000--16.333%
2016-05-18ANONYMOUSManual testing1000000000010000000000012---2.635--17.112%
2016-10-30ANONYMOUSManual testing2000000000020000000000012---5.270--18.401%
2016-10-30ANONYMOUSManual testing4000000000040000000000012---10.54--19.690%
2016-11-03ANONYMOUSManual testing100000000000100000000000012---26.35--21.392%
2017-01-04mikrS05260000000000480000000000012---56.27--24.279%


P+1 Factoring results:
dateuseridcompidb1b2startfactorSmoothdigitsbits*ghz-days
2021-05-13ATH5960X100000000024100000000027--2.725


Trial Factoring results:
 BitsFactorGHz-Daysworth
dateuseridcompidfromtofactorbits*digitsspentsaved
1999-09-22ANONYMOUSv4_computers252253--0.061--
1999-12-30ANONYMOUSv4_computers253254--0.122--
2000-03-01ANONYMOUSv4_computers254255--0.243--
2000-06-28ANONYMOUSv4_computers21256--0.974--
2000-06-29ANONYMOUSv4_computers21256--0.974--
2002-12-09ANONYMOUSv4_computers21257--1.948--
2016-02-23LaurVManual testing257258--1.948--
2010-07-20George WoltmanManual testing258259--3.895--
2010-07-20George WoltmanManual testing259260--7.791--
2012-11-08bcp19Manual testing260261--15.58--
2015-01-05LaurVManual testing261262--31.16--
2015-01-20LaurVManual testing262263--99.6--
2018-02-06snme2pm1g10263264--199.2--
2021-01-01Ruslan BorisovManual testing264265--379.1--
2022-06-15Anton RepkoManual testing264266--1,137--


ECM factoring results:
Total ECM effort:1,663.998 GHz-days
Estimated T-Level:49.572
DigitsB1CompleteFacMiss
20110005,330.4510.000%
25500001,933.3670.000%
30250000604.3230.000%
351000000145.1900.000%
40300000030.4050.000%
45110000005.6140.365%
50440000000.91440.074%
551100000000.13687.314%
602600000000.01898.195%
658000000000.00299.774%


ECM Summary

B1B2factorcurvesGHz-days
5000050000002800.036
250000250000006400.407
10000001000000001,5804.020
11000000110000000054215.17
44000000440000000014,4381,616
1100000001100000000010027.99


Lucas-Lehmer results:
dateuseridcompidres64spent (GHz-days)
1997-01-01George Woltman05646A61B1A6A75B1.20201e-6
2015-04-11MadPooManual testing05646A61B1A6A75B1.20201e-6


PRP results:
No PRP results for M9857


P-1 factor-bounds graph:
B1 = 60000000000, B2 = 4800000000000 (P-1 stage 2)
B1 = 100000000000, B2 = 1000000000000 (P-1 stage 2)
B1 = 100000000000 (P-1 stage 1)
B1 = 60000000000 (P-1 stage 1)
B1 = 40000000000, B2 = 400000000000 (P-1 stage 2)
B1 = 40000000000 (P-1 stage 1)
B1 = 20000000000, B2 = 200000000000 (P-1 stage 2)
B1 = 20000000000 (P-1 stage 1)
B1 = 10000000000, B2 = 100000000000 (P-1 stage 2)
B1 = 10000000000 (P-1 stage 1)
B1 = 1359491973, B2 = 80210026404 (P-1 stage 2)
B1 = 4290000000 (P-1 stage 1)
B1 = 3221225472, B2 = 4290000000 (P-1 stage 2)
B1 = 3221225472 (P-1 stage 1)
B1 = 3000000000, B2 = 4290000000 (P-1 stage 2)
B1 = 3000000000 (P-1 stage 1)
B1 = 2147483648, B2 = 4290000000 (P-1 stage 2)
B1 = 2147483648 (P-1 stage 1)
B1 = 1359491973 (P-1 stage 1)
B1 = 1073741824, B2 = 4290000000 (P-1 stage 2)
B1 = 1073741824 (P-1 stage 1)
B1 = 43000000, B2 = 4290000000 (P-1 stage 2)
B1 = 43000000 (P-1 stage 1)
B1 = 1000000, B2 = 100000000 (P-1 stage 2)
B1 = 1000000 (P-1 stage 1)
105
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109
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1011
105
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109
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1013
TF factor-bounds graph:
266
265
264
263
262
261
260
259
258
257
256
255
254
253
this exponent TF target: 44
TF double-checked to: 67.8
ECM T-Level=49.57 ~= 148-bit
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Last modified: 2023-04-26T21:34:10+00:00