M4 002 167 131 Mersenne number exponent details

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is 2 ^4002167131 - 1

has 1204772355 decimal digits

takes 1,004,062.208 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	250,607.7637	65.2174%	20000000	9600000000	197,146.2306	4.2362%	447,753.9943	66.6908%
Difference	-21	-250,607.6443	-10.2878%	-20000000	-9600000000	-197,146.2306	-4.2362%	-447,753.8748	-11.7613%

Known prime factors (4 factors, 181.4 bits, 0.00000453% 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
4002167131	40021671311	11	35.220	5 5	2012-08-20	1	5	1.157e-12	0.0004	0.0007
4002167131	192104022289	12	37.483	24 2³ × 3	2012-08-20	8	8	4.836e-12	0.0029	0.0059
4002167131	1814230386487873	16	50.688	226656 2⁵ × 3² × 787	2019-06-28	32	787	6.211e-8	0.0266	0.0290
4002167131	291397852842784097	18	58.016	36405008 2⁴ × 2275313	2019-12-23	16	2275313	1.526e-5	45.101	84.226

11 Composite Factors:

P-1 results:
No P-1 results for M4002167131

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2019-06-28			2³⁵	2³⁶	40021671311	35.220	11	1.36157e-14	236,449	2.91632e-14
2019-06-28			2³⁷	2³⁸	192104022289	37.483	12	2.61421e-13	236,449	5.59933e-13
2019-06-28			2⁵⁰	2⁵¹	1814230386487873	50.688	16	2.46279e-8	236,449	5.27502e-8
2019-12-23	slaur	palvi2-rtx	2¹	2⁶⁴	291397852842784097	58.016	18	0.001	220,786	0.002
Missing TF 64 - 65
Missing TF 65 - 66
Missing TF 66 - 67
Missing TF 67 - 68
2022-12-12	slaur	palvi2-rtx	2⁶⁸	2⁷¹		-	-	0.105	-	-

ECM factoring results:
No ECM results for M4002167131

Lucas-Lehmer results:
No L-L results for M4002167131

PRP results:
No PRP results for M4002167131

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

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TF factor-bounds graph:

2⁷¹

2⁶⁴

2⁵¹

2³⁸

2³⁶

this exponent TF target: 92

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2023-07-11T14:45:05+00:00