M4 031 047 931 Mersenne number exponent details

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is 2 ^4031047931 - 1

has 1213466342 decimal digits

takes 1,011,307.812 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	0.1186	54.9296%	-	-	-	-	0.1186	54.9296%
Target	2⁹²	248,812.2622	65.2174%	20000000	6000000000	125,796.0639	4.2391%	374,608.3261	66.6919%
Difference	-21	-248,812.1436	-10.2878%	-20000000	-6000000000	-125,796.0639	-4.2391%	-374,608.2075	-11.7623%

Known prime factors (1 factor, 54.4 bits, 0.00000135% 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
4031047931	23976713404067311	17	54.412	2974005 3² × 5 × 66089	2013-11-15	9	66089	1.169e-6	1.3129	2.4463

P-1 results:
No P-1 results for M4031047931

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2019-06-30			2⁵⁴	2⁵⁵	23976713404067311	54.412	17	5.74078e-7	2,053,280	0.034
2023-10-27	VladimirLapin	GTX1080	2³¹	2⁶⁸	23976713404067311	54.412	17	0.015	2,053,280	0.034
2023-01-07	slaur	palvi2-rtx	2⁶⁸	2⁷¹		-	-	0.104	-	-

ECM factoring results:
No ECM results for M4031047931

Lucas-Lehmer results:
No L-L results for M4031047931

PRP results:
No PRP results for M4031047931

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

10⁰

10¹

10²

10³

10⁴

10⁵

TF factor-bounds graph:

2⁷¹

2⁶⁸

2⁵⁵

this exponent TF target: 92

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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Last modified: 2023-10-27T18:34:25+00:00