M4 004 213 131 Mersenne number exponent details

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is 2 ^4004213131 - 1

has 1205388262 decimal digits

takes 1,004,575.507 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	0.1194	54.9296%	-	-	-	-	0.1194	54.9296%
Target	2⁹²	250,479.7127	65.2174%	20000000	9600000000	197,146.2306	4.2364%	447,625.9433	66.6909%
Difference	-21	-250,479.5934	-10.2878%	-20000000	-9600000000	-197,146.2306	-4.2364%	-447,625.8239	-11.7613%

Known prime factors (3 factors, 129.9 bits, 0.00000324% 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
4004213131	192202230289	12	37.484	24 2³ × 3	2012-08-20	8	8	4.834e-12	0.0029	0.0059
4004213131	744783642367	12	39.438	93 3 × 31	2019-06-28	3	31	2.234e-11	0.0016	0.0022
4004213131	8770612214633327	16	52.962	1095173 1095173	2019-06-28	1	1095173	2.330e-7	21.706	40.540

4 Composite Factors:

P-1 results:
No P-1 results for M4004213131

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2019-06-28			2³⁷	2³⁸	192202230289	37.484	12	2.61287e-13	236,554	5.59609e-13
2019-06-28			2³⁹	2⁴⁰	744783642367	39.438	12	4.04995e-12	236,554	8.67394e-12
2019-06-28			2⁵²	2⁵³	8770612214633327	52.962	16	8.31214e-8	236,554	1.78024e-7
TF systematically completed to 64 but no per-exponent detailed record exists
2022-12-14	slaur	palvi2-rtx	2⁶⁸	2⁷¹		-	-	0.105	-	-

ECM factoring results:
No ECM results for M4004213131

Lucas-Lehmer results:
No L-L results for M4004213131

PRP results:
No PRP results for M4004213131

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

10⁶

10⁷

TF factor-bounds graph:

2⁷¹

2⁵³

2⁴⁰

2³⁸

this exponent TF target: 92

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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