is 2 13709 - 1
has 4127 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
Actual2672,167.475279.1045%10000000002480162209024503,864.500928.0927%6,031.976184.9746%
Target2440.000268.1818%500100000.00001.3916%0.000268.6246%
Difference+23+2,167.4750+10.9227%+999999500+248016220892450+3,864.5009+26.7011%+6,031.9759+16.3500%

Known prime factors (6 factors, 348.0 bits, 2.53883434% known):
Remaining cofactor is not a probable-prime

P-1GHz-days
exponentfactordigitsbits*kdate foundmin B1min B2min. TFmin. P-1normal P-1
13709212736263927.6647759
7759
-177592.190e-91.212e-72.258e-7
1370911219445611030.06340920
23 × 3 × 5 × 11 × 31
2008-08-2611311.938e-83.457e-96.402e-9
1370915528242426171340.49856635212
22 × 3 × 1783 × 2647
2008-08-26178326471.821e-55.234e-71.038e-6
1370955080304629317487707512272.222200891037381710875
53 × 79 × 1549 × 20359 × 645083
2008-08-2620359645083128,5831.556e-51.877e-5
13709259822706874848880949393912684.426947635520004554967355
5 × 7 × 11 × 2461390961050792123
2008-08-29112461390961050792123452,497,66538,349,83971,626,819
13709111820132201877576086278313272993.175407834751629869341623307
32 × 7 × 11 × 61 × 193 × 2342269 × 21341605127
2009-07-292342269213416051272.707e+110.33310.6210

57 Composite Factors:
P-1 results:
 GHz-DaysworthFactor
probability
dateuseridcompidb1b2estagefactordigitsbits*spentsaved
2021-08-27Seth_TrManual testing400000000400000000-
skipped known factor: 212736263
skipped known factor: 1121944561
skipped known factor: 1552824242617
skipped known factor: 5508030462931748770751
--0.114--7.825%
2022-03-04Ethan O'ConnorManual testing1000000000248016220902450-
skipped known factor: 212736263
skipped known factor: 1121944561
skipped known factor: 1552824242617
skipped known factor: 5508030462931748770751
skipped known factor: 11182013220187757608627831327
--3,865--28.093%


Trial Factoring results:
 BitsFactorGHz-Daysworth
dateuseridcompidfromtofactorbits*digitsspentsaved
2008-08-26ANONYMOUSManual testing??30.063108.94357e-90.0005.84274e-7
2008-08-26ANONYMOUSManual testing??40.498137.52084e-60.0000.000


ECM factoring results:
Total ECM effort:43.405 GHz-days
Estimated T-Level:38.570
DigitsB1CompleteFacMiss
2011000698.8820.000%
2550000165.6240.000%
3025000031.9620.000%
3510000005.1270.593%
4030000000.71448.965%
45110000000.08891.608%
50440000000.01099.029%


ECM Summary

B1B2factorcurvesGHz-days
10.00000e+0
10.00000e+0
10.00000e+0
5000050000001480.030
250000250000005410.557
50000050000000110.023
10000001000000001,4215.848
30000003000000002793.444
30000005280000001,00015.40
11000000110000000040018.11


Lucas-Lehmer results:
No L-L results for M13709


PRP results:
dateuseridcompidcofactorsres64PRP
2017-09-21Oliver KruseOliver-PC
212736263
1121944561
1552824242617
5508030462931748770751
25982270687484888094939391
11182013220187757608627831327
5725FAF2D5161341no
2017-09-21Oliver KruseManual testing
212736263
1121944561
1552824242617
5508030462931748770751
25982270687484888094939391
11182013220187757608627831327
5725FAF2D5161341no
2017-10-02kkmrkkblmbrbkManual testing
212736263
1121944561
1552824242617
5508030462931748770751
25982270687484888094939391
11182013220187757608627831327
5725FAF2D51613__no
2017-12-07ATHManual testing
212736263
1121944561
1552824242617
5508030462931748770751
25982270687484888094939391
11182013220187757608627831327
5725FAF2D51613__no
2020-04-17Oliver KruseManual testing
212736263
1121944561
1552824242617
5508030462931748770751
25982270687484888094939391
11182013220187757608627831327
BF3AB3C4FEFB2E__no


P-1 factor-bounds graph:
B1 = 1000000000, B2 = 248016220902450 (P-1 stage 2)
B1 = 1000000000 (P-1 stage 1)
B1 = 400000000 (P-1 stage 1)
100
101
102
103
104
105
106
107
108
109
100
101
102
103
104
105
106
107
108
109
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
TF factor-bounds graph:
2
this exponent TF target: 44
TF double-checked to: 67.7
ECM T-Level=38.57 ~= 112-bit
250
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290
2100
2110
2120
Last modified: 2023-03-23T17:39:31+00:00