M4 002 167 083 Mersenne number exponent details

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is 2 ^4002167083 - 1

has 1204772340 decimal digits

takes 1,004,062.195 GHz-days to do one PRP test

0 primality tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷¹	0.1195	54.9296%	-	-	-	-	0.1195	54.9296%
Target	2⁹²	250,607.7668	65.2174%	20000000	6000000000	125,796.0639	4.2362%	376,403.8306	66.6908%
Difference	-21	-250,607.6473	-10.2878%	-20000000	-6000000000	-125,796.0639	-4.2362%	-376,403.7112	-11.7613%

Known prime factors (1 factor, 55.0 bits, 0.00000137% known):

Remaining cofactor is PRP status unknown

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4002167083	36032854976388889	17	55.0002	4501668 2² × 3 × 17 × 22067	2013-08-29	17	22067	1.508e-6	0.4432	0.8167

P-1 results:
No P-1 results for M4002167083

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2022-12-12	slaur	palvi2-rtx	2⁶⁸	2⁷¹		-	-	0.105	-	-

ECM factoring results:
No ECM results for M4002167083

Lucas-Lehmer results:
No L-L results for M4002167083

PRP results:
No PRP results for M4002167083

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

TF factor-bounds graph:

2⁷¹

this exponent TF target: 92

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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