is 2 3109333 - 1
has 936003 decimal digits
takes 0.265 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
Actual27076.849568.5714%3950000314527521021.609010.9825%98.458572.0231%
Target2641.144765.6250%140002400000.00321.5080%1.148066.1434%
Difference+6+75.7048+2.9464%+3936000+3145035210+21.6058+9.4745%+97.3106+5.8797%

Known prime factors (5 factors, 190.0 bits, 0.00610949% known):
Remaining cofactor is not a probable-prime

P-1GHz-days
exponentfactordigitsbits*kdate foundmin B1min B2min. TFmin. P-1normal P-1
310933318655999824.1533
3
-137.193e-131.369e-72.512e-7
310933368405327826.02811
11
2008-09-071112.882e-121.906e-72.512e-7
3109333124373321926.89020
22 × 5
2008-09-07452.888e-125.004e-71.005e-6
3109333308078372626071444.8084954091
4954091
2008-09-30149540919.905e-70.03330.0622
31093333130882657822702921612168.08550346531841760
25 × 5 × 7 × 11 × 8719 × 468697
2019-12-07871946869731.9870.00420.0059

26 Composite Factors:
P-1 results:
 GHz-DaysworthFactor
probability
dateuseridcompidb1b2estagefactordigitsbits*spentsaved
2019-12-07Jocelyn LaroucheManual testing518205000002168.0850.0090.5290.0191.150%
2020-07-02Jocelyn LaroucheManual testing32500062186666-
skipped known factor: 18655999
skipped known factor: 68405327
skipped known factor: 124373321
skipped known factor: 30807837262607
skipped known factor: 313088265782270292161
--0.080--3.166%
2020-07-06Jocelyn LaroucheManual testing3250001554666512-
skipped known factor: 18655999
skipped known factor: 68405327
skipped known factor: 124373321
skipped known factor: 30807837262607
skipped known factor: 313088265782270292161
--0.142--3.813%
2021-08-11Jocelyn LaroucheManual testing31093333109333-
skipped known factor: 18655999
skipped known factor: 68405327
skipped known factor: 124373321
skipped known factor: 313088265782270292161
--0.384--3.087%
2021-08-12Jocelyn LaroucheManual testing31093333109333012-
skipped known factor: 18655999
skipped known factor: 68405327
skipped known factor: 124373321
skipped known factor: 30807837262607
skipped known factor: 313088265782270292161
--0.572--5.564%
2021-08-23Jocelyn LaroucheManual testing310933315546665012-
skipped known factor: 18655999
skipped known factor: 68405327
skipped known factor: 124373321
skipped known factor: 30807837262607
skipped known factor: 313088265782270292161
--1.408--7.344%
2021-12-21Jocelyn LaroucheManual testing3950000116747400-
skipped known factor: 18655999
skipped known factor: 68405327
skipped known factor: 124373321
skipped known factor: 30807837262607
skipped known factor: 313088265782270292161
--1.246--7.159%
2022-03-20Jocelyn LaroucheManual testing39500001042528410-
skipped known factor: 18655999
skipped known factor: 68405327
skipped known factor: 124373321
skipped known factor: 30807837262607
skipped known factor: 313088265782270292161
--7.471--9.697%
2022-07-20Jocelyn LaroucheManual testing39500003145275210-
skipped known factor: 18655999
skipped known factor: 68405327
skipped known factor: 124373321
skipped known factor: 30807837262607
skipped known factor: 313088265782270292161
--21.61--10.983%


Trial Factoring results:
 BitsFactorGHz-Daysworth
dateuseridcompidfromtofactorbits*digitsspentsaved
2008-09-07Will EdgingtonManual testing??26.89091.24470e-141.6777.88875e-14
2008-09-07Will EdgingtonManual testing??26.02886.84584e-151.6774.33881e-14
2008-09-30markrManual testing??44.808142.36724e-71.6771.50032e-6
2021-01-02Jocelyn LaroucheManual testing264265--1.202--
2021-01-20Jocelyn LaroucheManual testing265266--2.403--
2021-01-27Jocelyn LaroucheManual testing266267--4.807--
2021-01-27Jocelyn LaroucheManual testing267268--9.61--
2021-01-27Jocelyn LaroucheManual testing268269
skipped known factors(?)
--19.23--
2021-08-21Jocelyn LaroucheManual testing269270--38.45--


ECM factoring results:
Total ECM effort:0.351 GHz-days
Estimated T-Level:0.577
DigitsB1CompleteFacMiss
20110000.11589.102%
25500000.01198.938%


ECM Summary

B1B2factorcurvesGHz-days
50000500000030.351


Lucas-Lehmer results:
No L-L results for M3109333


PRP results:
dateuseridcompidcofactorsres64PRP
2017-10-29Oliver KruseGTX-3
18655999
68405327
124373321
30807837262607
EA550843B4F68A__no
2017-12-11kkmrkkblmbrbkc4.xlarge
18655999
68405327
124373321
30807837262607
EA550843B4F68A__no
2019-12-07mrhx
18655999
68405327
124373321
30807837262607
313088265782270292161
EA550843B4F68AA1no


P-1 factor-bounds graph:
B1 = 3950000, B2 = 3145275210 (P-1 stage 2)
B1 = 3950000, B2 = 1042528410 (P-1 stage 2)
B1 = 3109333, B2 = 155466650 (P-1 stage 2)
B1 = 3950000, B2 = 116747400 (P-1 stage 2)
B1 = 3109333, B2 = 31093330 (P-1 stage 2)
B1 = 3950000 (P-1 stage 1)
B1 = 3109333 (P-1 stage 1)
B1 = 325000, B2 = 15546665 (P-1 stage 2)
B1 = 325000, B2 = 6218666 (P-1 stage 2)
B1 = 325000 (P-1 stage 1)
B1 = 51820, B2 = 500000 (P-1 stage 2)
B1 = 51820 (P-1 stage 1)
100
101
102
103
104
105
106
107
100
101
102
103
104
105
106
107
108
109
1010
TF factor-bounds graph:
270
269
268
267
266
265
2
this exponent TF target: 64
TF double-checked to: 67.8
ECM T-Level=0.58 ~= -15-bit
250
260
270
Last modified: 2023-04-26T21:34:10+00:00