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M3 441 967 Mersenne number exponent details
is 2 3441967 - 1
has 1036136 decimal digits
takes 0.362 GHz-days to do one PRP test
Last-known PrimeNet details:
Exponent is not assigned to anyone
factored, 0 LL tests remaining
ResidueStatus
L-L701ECC372AE5F957double-checked
PRP-unknown--unknown-

 Trial FactoringP-1 FactoringCombined
LimitGHz-daysProbabilityB1B2GHz-daysProbabilityGHz-daysProbability
Actual2678.632867.1642 %10000001146568501.09538.1874 %9.728269.8526 %
Target2641.034165.6250 %1900017000000.01681.8540 %1.050966.2623 %
Difference+3+7.5987+1.5392 %+981000+112956850+1.0785+6.3335%+8.6772+3.5903 %

Known prime factors (1 factor, 65.4 bits, 0.00190044% known):
Remaining cofactor is not a probable-prime

P-1GHz-days
exponentfactordigitsbits*kdate foundmin B1min B2min. TFmin. P-1normal P-1
3441967491059265620506922072065.4137133410425209
37 × 347 × 823 × 675097
2010-10-238236750972.11960.00570.0105

P-1 results:
dateusercompB1B2BSstagefactordigitsbits*GHz-daysFac Prob
2010-10-09Rob_Deetwopc1000020000--0.0020.527%
2010-10-10Rob_Deetwopc2000030000--0.0030.736%
2010-10-11Rob_Deetwopc3000040000--0.0050.897%
2010-10-12Rob_Deetwopc4000050000--0.0061.032%
2010-10-13Rob_Deetwopc5000060000--0.0081.150%
2010-10-14Rob_Deetwopc6000070000--0.0091.255%
2010-10-15Rob_Deetwopc7000080000--0.0111.351%
2010-10-16Rob_Deetwopc8000090000--0.0121.439%
2010-10-17Rob_Deetwopc90000100000--0.0141.520%
2010-10-18Rob_Deetwopc100000200000--0.0162.076%
2010-10-19Rob_Deetwopc100000300000--0.0172.408%
2010-10-20Rob_Deetwopc100000400000--0.0182.646%
2010-10-21Rob_Deetwopc100000500000--0.0192.832%
2010-10-22Rob_Deetwopc100000600000--0.0192.986%
2010-10-23Rob_Deetwopc2065.4130.0200.000%
2021-03-16JossManual testing34419637861636
skipped known factor: 49105926562050692207
---5.364%
2021-03-17JossManual testing34419637861636
skipped known factor: 49105926562050692207
---5.364%
2022-01-22JossManual testing1000000114656850
skipped known factor: 49105926562050692207
--1.14710.484%


Trial Factoring results:
575859606162636465666768
 BitsFactor
dateuseridcompidfromtofactorbits*digitsGHz-days
2001-07-29David Campeauv4_computers212600.022
2009-03-21S485122USB-Z2602610.045
2022-05-11LordJuliusManual testing21262
2022-05-11LordJuliusManual testing262263
2022-05-11LordJuliusManual testing263264
2022-05-11LordJuliusManual testing264265
2022-05-11LordJuliusManual testing266267
2021-06-10JossManual testing267268


ECM factoring results:
Total ECM effort:0.299 GHz-days
Estimated T-Level:0.577
DigitsB1CompleteFacMiss
20110000.11589.102%
25500000.01198.938%


ECM Summary

B1B2factorcurvesGHz-days
50000500000030.299


Lucas-Lehmer results:
dateuseridcompidres64spent (GHz-days)
1999-09-30ANONYMOUSv4_computers701ECC372AE5F9570.362


PRP results:
dateuseridcompidcofactorsres64
2017-11-06Oliver KruseGTX-0
49105926562050692207
9348B6B57A90721B
2017-12-16kkmrkkblmbrbkc4.xlarge
49105926562050692207
9348B6B57A90721B


CERT results:
No CERT results for M3441967


P-1 factor-bounds graph:
B1 = 1000000, B2 = 114656850 (P-1 stage 2)
B1 = 1000000 (P-1 stage 1)
B1 = 344196, B2 = 3786163 (P-1 stage 2)
B1 = 344196 (P-1 stage 1)
B1 = 100000, B2 = 600000 (P-1 stage 2)
B1 = 100000, B2 = 500000 (P-1 stage 2)
B1 = 100000, B2 = 400000 (P-1 stage 2)
B1 = 100000, B2 = 300000 (P-1 stage 2)
B1 = 100000, B2 = 200000 (P-1 stage 2)
B1 = 100000 (P-1 stage 1)
B1 = 90000, B2 = 100000 (P-1 stage 2)
B1 = 90000 (P-1 stage 1)
B1 = 80000, B2 = 90000 (P-1 stage 2)
B1 = 80000 (P-1 stage 1)
B1 = 70000, B2 = 80000 (P-1 stage 2)
B1 = 70000 (P-1 stage 1)
B1 = 60000, B2 = 70000 (P-1 stage 2)
B1 = 60000 (P-1 stage 1)
B1 = 50000, B2 = 60000 (P-1 stage 2)
B1 = 50000 (P-1 stage 1)
B1 = 40000, B2 = 50000 (P-1 stage 2)
B1 = 40000 (P-1 stage 1)
B1 = 30000, B2 = 40000 (P-1 stage 2)
B1 = 30000 (P-1 stage 1)
B1 = 20000, B2 = 30000 (P-1 stage 2)
B1 = 20000 (P-1 stage 1)
B1 = 10000, B2 = 20000 (P-1 stage 2)
B1 = 10000 (P-1 stage 1)
101
102
103
104
105
106
101
102
103
104
105
106
107
108
109
TF factor-bounds graph:
268
267
265
264
263
262
261
260
this exponent TF target: 64
TF double-checked to: 67
ECM T-Level=0.58 ~= -15-bit
250
260
270
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Last modified: 2024-02-09T03:30:02+00:00