M82 939 Mersenne number exponent details

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is 2 ⁸²⁹³⁹ - 1

has 24968 decimal digits

takes 0.000 GHz-days to do one PRP test

Has been fully factored.

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
PRP	-unknown-	-unknown-
Cofactor is a certified prime

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	unknown			-	-	-	-	0.0000	0.0000%
Target	2⁴⁴	0.0000	61.3636%	500	50000	0.0000	2.3547%	0.0000	62.2734%
Difference	-44	0.0000	-61.3636%	-500	-50000	0.0000	-2.3547%	0.0000	-62.2734%

Known prime factors (3 factors, 82,939.0 bits, 100.00000000% known):

Remaining cofactor is a certified-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
82939	867140681119	12	39.657	5227581 3 × 1742527	-	3	1742527	1.334e-6	0.0002	0.0004
82939	1018662740943783967	19	59.821	6141035827197 3² × 43 × 15868309631	2009-07-15	43	15868309631	0.9494	1.8804	3.5121
82939	hide decimal representation P24938 click to show decimal representation	24,938	82,839.521		2009-07-15

1 Composite Factors:

P-1 results:
No P-1 results for M82939

Trial Factoring results:
No TF results for M82939

ECM factoring results:

Total ECM effort:	0.454 GHz-days
Estimated T-Level:	25.325

Digits	B1	Complete	FacMiss
20	11000	11.154	0.001%
25	50000	1.032	35.628%
30	250000	0.065	93.698%
35	1000000	0.003	99.696%

ECM Summary

B1	B2	factor	curves	GHz-days
		1018662740943783967	1	0.00000e+0
50000	5000000		290	0.454

Lucas-Lehmer results:
No L-L results for M82939

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-30

ATH

ec2-1x

867140681119

1018662740943783967

PRP

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

10⁰

10¹

10²

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.9

ECM T-Level=25.33 ~= 68-bit

2⁵⁰

2⁶⁰

2⁷⁰

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Last modified: 2023-10-02T12:12:48+00:00