M2 837 Mersenne number exponent details

≡

is 2 ²⁸³⁷ - 1

has 855 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	2⁶⁷	10,473.7108	82.0896%	-	-	-	-	10,473.7108	82.0896%
Target	2⁴⁴	0.0008	72.7273%	500	50000	0.0000	0.8510%	0.0008	72.9594%
Difference	+23	+10,473.7100	+9.3623%	-500	-50000	0.0000	-0.8510%	+10,473.7100	+9.1302%

Known prime factors (4 factors, 2,837.0 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
2837	22697	5	14.470	4 2²	-	4	4	7.699e-13	1.697e-10	3.453e-10
2837	138871151	9	27.049	24475 5² × 11 × 89	2009-03-05	25	89	8.178e-9	1.208e-9	2.158e-9
2837	336396730297	12	38.291	59287404 2² × 3 × 11 × 101 × 4447	2009-03-05	101	4447	2.286e-5	1.433e-8	1.918e-8
2837	hide decimal representation P830 click to show decimal representation	830	2,757.189		2009-03-05

4 Composite Factors:

P-1 results:
No P-1 results for M2837

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-03-05	ANONYMOUS	Manual testing	?	?	138871151	27.049	9	1.87575e-9	0.001	1.86774e-5
2009-03-05	ANONYMOUS	Manual testing	?	?	336396730297	38.291	12	9.95726e-6	0.001	0.096

ECM factoring results:
No ECM results for M2837

Lucas-Lehmer results:
No L-L results for M2837

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-09

kkmrkkblmbrbk

c4.large

22697

138871151

336396730297

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

10³

10⁰

10¹

10²

10³

10⁴

TF factor-bounds graph:

2

this exponent TF target: 44

TF double-checked to: 67.9

2⁵⁰

2⁶⁰

2⁷⁰

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