is 2 1408409 - 1
has 423974 decimal digits
takes 0.054 GHz-days to do one PRP test
Last-known PrimeNet details:
Exponent is not assigned to anyone
0 primality tests remaining
ResidueStatus
L-LA8BDF95A08AC377Adouble-checked
PRP-unknown--unknown-

 Trial FactoringP-1 FactoringCombined
LimitGHz-daysProbabilityB1B2GHz-daysProbabilityGHz-daysProbabilityProb over default TF
Actual26721.097568.6567%500000150000000.07144.9108%21.168970.1959%1.5392%
PrimeNet2560.006862.5000%65001100000.00072.7654%0.007563.5370%1.0370%
GPU722600.109165.0000%6000700000.00051.2442%0.109665.4355%0.4355%
Difference+7+20.9885+3.6567%+494000+14930000+0.0709+3.6666%+21.0593+4.7604%+4.7604%

Known prime factors (2 factors, 152.7 bits, 0.01084418% known):
Remaining cofactor is not a probable-prime

P-1GHz-days
exponentfactordigitsbits*kdate foundmin B1min B2min. TFmin. P-1normal P-1
1408409728619832966664592134812375.94825866769985375860
22 × 5 × 67 × 48859 × 395087081
2009-02-22488593950870818,514.11.19422.2257
14084091299966663199262954192812476.78346150183050493960
23 × 5 × 43 × 349 × 76881093907
2019-01-113497688109390716,605231.89433.11

1 Composite Factors:
exponentprime factorscomposite factordigitsbits*
1408409947181493002479300478154361989320006838252716146152.730
P-1 results:
 GHz-DaysworthFactor
probability
dateuseridcompidb1b2estagefactordigitsbits*spentsaved
2003-09-21T00:00:00ANONYMOUSv4_computers15000228750---0.001--0.817%
2016-03-17T19:13:55alpertronManual testing5000001500000012---0.071--4.911%


Trial Factoring results:
 BitsFactorGHz-Daysworth
dateuseridcompidfromtofactorbits*digitsspentsaved
2001-10-25T00:00:00ANONYMOUSv4_computers21257--0.014--
2003-07-13T00:00:00ANONYMOUSv4_computers21258--0.027--
2022-03-07T17:32:42LordJuliusManual testing258260--0.082--
2009-02-19T20:15:00Sturle Sundehaydn.ifi260261--0.109--


ECM factoring results:

Old Calculation Method

Total ECM effort:25.253 GHz-days
Estimated T-Level:25.391
DigitsB1CurvesCompleteFacMiss
2011000298 / 1002.9805.004%
2550000298 / 2801.06434.432%
3025000050 / 6400.07892.479%

New Calculation Method

Total ECM effort:25.253 GHz-days
Estimated T-Level:25.391
DigitsB1CompleteFacMiss
201100014.5380.000%
25500001.64019.395%
302500000.14086.925%
3510000000.01099.024%


ECM Summary

B1B2factorcurvesGHz-days
10.00000e+0
5000050000001677.865
500005000000813.815
250000350000005013.57


Lucas-Lehmer results:
No L-L results for M1408409


PRP results:
dateuseridcompidcofactorsres64PRP
2017-09-30T17:33:08Oliver KruseGTX-1
72861983296666459213481
F4CE6E8977376F__no
2017-10-26T05:29:12kkmrkkblmbrbkold
72861983296666459213481
F4CE6E8977376F__no
2019-01-12T01:57:03Oliver KruseGTX-1
72861983296666459213481
129996666319926295419281
10AC8847085E8044no
2019-01-12T09:21:36marssystemssystem03
72861983296666459213481
129996666319926295419281
10AC8847085E8044no


P-1 factor-bounds graph:
B1 = 500000, B2 = 15000000 (P-1 stage 2)
B1 = 500000 (P-1 stage 1)
B1 = 15000, B2 = 228750 (P-1 stage 2)
B1 = 15000 (P-1 stage 1)
101
102
103
104
105
106
101
102
103
104
105
106
107
108
109
1010
1011
TF factor-bounds graph:
267
261
260
258
257
250
260
270
280
290
2100
Last modified: 2022-03-07T17:32:42+00:00