M577 Mersenne number exponent details

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is 2 ⁵⁷⁷ - 1

has 174 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	08CDCF0BAB11AB1F	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	0.0041	77.2727%	500	50000	0.0000	0.5038%	0.0041	77.3872%
Difference	-44	-0.0041	-77.2727%	-500	-50000	0.0000	-0.5038%	-0.0041	-77.3872%

Known prime factors (3 factors, 577.0 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
577	3463	4	11.758	3 3	-	1	3	4.727e-13	1.635e-11	3.000e-11
577	132305774316967	15	46.911	114649717779 3² × 709 × 17967359	-	709	17967359	0.0200	1.444e-5	2.695e-5
577	hide decimal representation P157 click to show decimal representation	157	518.331

1 Composite Factors:

P-1 results:
No P-1 results for M577

Trial Factoring results:
No TF results for M577

ECM factoring results:
No ECM results for M577

Lucas-Lehmer results:
No L-L results for M577

PRP results:

date	userid	compid	cofactors	res64	PRP
2018-01-24	Luke_Richards	work-laptop		08CDCF0BAB11AB1F	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

10³

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.9

2⁵⁰

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