is 2 40853 - 1
has 12298 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
Actual267727.337576.1194 %89000000073554676598403041,483.665530.7581 %42,211.003083.4646 %
Target2440.000163.6364 %500500000.00001.9244 %0.000164.3362 %
Difference+23+727.3374+12.4830 %+889999500+735546765934030+41,483.6655+28.8336%+42,211.0029+19.1284 %

Known prime factors (2 factors, 77.7 bits, 0.19010739% known):
Remaining cofactor is not a probable-prime

P-1GHz-days
exponentfactordigitsbits*kdate foundmin B1min B2min. TFmin. P-1normal P-1
408531225591720.22515
3 × 5
-353.419e-123.218e-96.320e-9
408531954429499318444711857.4402392026900495
3 × 5 × 17 × 43457 × 215857
2008-08-26434572158570.46995.471e-59.155e-5

1 Composite Factors:
P-1 results:
dateusercompB1B2BSstagefactordigitsbits*GHz-daysFac Prob
2016-09-13kkmrkkblmbrbkManual testing100000000200000000012
skipped known factor: 1225591
skipped known factor: 195442949931844471
---39.122%
2021-12-18Lisander ViaeneDesktop10000000001000000000
skipped known factor: 1225591
skipped known factor: 195442949931844471
--1.03534.664%
2023-04-07JacobZMServer890000000735546765984030
skipped known factor: 1225591
skipped known factor: 195442949931844471
--57,30270.501%


P+1 Factoring results:
dateuseridcompidb1b2startfactorSmoothdigitsbits*ghz-days
2021-05-02ATHcolab-Pp11000000001000000000027--0.705


Trial Factoring results:
5758596061626364656667
No TF results for M40853


ECM factoring results:
Total ECM effort:64.884 GHz-days
Estimated T-Level:35.614
DigitsB1CompleteFacMiss
2011000326.7180.000%
255000062.6180.000%
302500009.4930.008%
3510000001.17930.750%
4030000000.12388.450%
45110000000.01198.913%


ECM Summary

B1B2factorcurvesGHz-days
10.001
5000050000002830.192
250000250000005832.171
10000001000000001,47722.00
3000000114863248505040.52


Lucas-Lehmer results:
No L-L results for M40853


PRP results:
dateuseridcompidcofactorsres64
2017-09-21Oliver KruseOliver-PC
1225591
195442949931844471
6477081810298F06
2017-09-21Oliver KruseManual testing
1225591
195442949931844471
6477081810298F06
2017-10-13kkmrkkblmbrbkManual testing
1225591
195442949931844471
6477081810298F06
2020-04-17Oliver KruseManual testing
1225591
195442949931844471
295B0F5B15DCE2D2


CERT results:
No CERT results for M40853


P-1 factor-bounds graph:
B1 = 890000000, B2 = 735546765984030 (P-1 stage 2)
B1 = 1000000000 (P-1 stage 1)
B1 = 890000000 (P-1 stage 1)
B1 = 100000000, B2 = 2000000000 (P-1 stage 2)
B1 = 100000000 (P-1 stage 1)
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TF factor-bounds graph:
this exponent TF target: 44
TF double-checked to: 67
ECM T-Level=35.61 ~= 102-bit
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Last modified: 2024-03-13T02:15:48+00:00