is 2 8609 - 1
has 2592 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-L-unknown--unknown-
PRP-unknown--unknown-

 Trial FactoringP-1 FactoringCombined
LimitGHz-daysProbabilityB1B2GHz-daysProbabilityGHz-daysProbability
Actual2673,451.494779.1045 %680000000002654226487924011002,556,989.947240.8256 %2,560,441.441887.6352 %
Target2440.000368.1818 %500500000.00001.2068 %0.000368.5658 %
Difference+23+3,451.4944+10.9227 %+67999999500+265422648792351100+2,556,989.9472+39.6188%+2,560,441.4416+19.0694 %

Known prime factors (1 factor, 125.9 bits, 1.46213117% known):
Remaining cofactor is not a probable-prime

P-1GHz-days
exponentfactordigitsbits*kdate foundmin B1min B2min. TFmin. P-1normal P-1
86097800319245352283889291666360698632896738125.8754530328287462123294977155512079587
32 × 7 × 11 × 14767 × 31357 × 80511407 × 175352613137123
-805114071753526131371232.125e+131,689.33,155.1

P-1 results:
dateusercompB1B2BSstagefactordigitsbits*GHz-daysFac Prob
2001-02-11ANONYMOUSv4_computers1000000100000000--0.00126.541%
2001-06-23ANONYMOUSv4_computers430000004290000000--0.04938.528%
2001-09-10ANONYMOUSv4_computers30000000004290000000--0.54336.341%
2002-06-09ANONYMOUSv4_computers1073741824429000000048--0.22137.479%
2002-08-31ANONYMOUSv4_computers2147483648429000000048--0.40036.761%
2002-10-26ANONYMOUSv4_computers3221225472429000000048--0.58036.245%
2003-02-16ANONYMOUSv4_computers42900000004290000000--0.75935.838%
2023-08-14JacobZGreatLakes68000000000265422648792401100
skipped known factor: 78003192453522838892916663606986328967
--6,709,91080.037%


Trial Factoring results:
5758596061626364656667
 BitsFactor
dateuseridcompidfromtofactorbits*digitsGHz-days
1999-09-22ANONYMOUSv4_computers2522530.070
1999-12-30ANONYMOUSv4_computers2532540.139
2000-02-23ANONYMOUSv4_computers2542550.279
2000-07-25ANONYMOUSv4_computers212561.115
2002-12-16ANONYMOUSv4_computers212572.230


ECM factoring results:
Total ECM effort:3,866.667 GHz-days
Estimated T-Level:46.838
DigitsB1CompleteFacMiss
20110006,174.8000.000%
25500001,760.2860.000%
30250000489.2000.000%
351000000103.1610.000%
40300000018.1830.000%
45110000002.7636.309%
50440000000.36869.236%
551100000000.04495.712%
602600000000.00599.534%


ECM Summary

B1B2factorcurvesGHz-days
30000003000000008747.172
110000003657888466212,0003,859


Lucas-Lehmer results:
No L-L results for M8609


PRP results:
dateuseridcompidcofactorsres64
2017-09-21Oliver KruseOliver-PC
78003192453522838892916663606986328967
91891717E6A29A06
2017-09-21Oliver KruseManual testing
78003192453522838892916663606986328967
91891717E6A29A06
2017-10-12kkmrkkblmbrbkManual testing
78003192453522838892916663606986328967
91891717E6A29A06
2020-04-17Oliver KruseManual testing
78003192453522838892916663606986328967
FBDA40E5B3C7C4CA


CERT results:
No CERT results for M8609


P-1 factor-bounds graph:
B1 = 68000000000, B2 = 265422648792401100 (P-1 stage 2)
B1 = 68000000000 (P-1 stage 1)
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 = 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)
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1010
1011
105
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TF factor-bounds graph:
257
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253
this exponent TF target: 44
TF double-checked to: 67
ECM T-Level=46.84 ~= 139-bit
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Last modified: 2024-03-13T02:15:48+00:00