M457 Mersenne number exponent details

≡

is 2 ⁴⁵⁷ - 1

has 138 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

factored, 0 PRP tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
PRP	6DDFA1843FFF8CD2	PRP-tested
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	0.0051	79.5455%	500	50000	0.0000	0.4655%	0.0051	79.6407%
Difference	-44	-0.0051	-79.5455%	-500	-50000	0.0000	-0.4655%	-0.0051	-79.6407%

Known prime factors (2 factor, 457.0 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
457	150327409	9	27.164	164472 2³ × 3 × 7 × 11 × 89	-	11	89	6.260e-8	2.248e-10	3.300e-10
457	hide decimal representation P130 click to show decimal representation	130	429.836

P-1 results:
No P-1 results for M457

Trial Factoring results:
No TF results for M457

ECM factoring results:
No ECM results for M457

Lucas-Lehmer results:
No L-L results for M457

PRP results:

date	userid	compid	cofactors	res64	PRP
2018-01-24	Luke_Richards	work-laptop		6DDFA1843FFF8CD2	no

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

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.9

2⁵⁰

JSON version of this page

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