M4 015 431 631 Mersenne number exponent details

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is 2 ^4015431631 - 1

has 1208765367 decimal digits

takes 1,007,390.000 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	0.1191	54.9296%	-	-	-	-	0.1191	54.9296%
Target	2⁹²	249,779.9109	65.2174%	20000000	9600000000	197,146.2306	4.2375%	446,926.1414	66.6913%
Difference	-21	-249,779.7918	-10.2878%	-20000000	-9600000000	-197,146.2306	-4.2375%	-446,926.0224	-11.7617%

Known prime factors (2 factors, 91.2 bits, 0.00000227% 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
4015431631	232895034599	12	37.761	29 29	2012-08-20	1	29	4.875e-12	0.0009	0.0009
4015431631	12240770277752593	17	53.443	1524216 2³ × 3 × 41 × 1549	2019-06-29	41	1549	3.244e-7	0.0448	0.0572

1 Composite Factors:

P-1 results:
No P-1 results for M4015431631

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2019-06-29			2³⁷	2³⁸	232895034599	37.761	12	3.14840e-13	237,129	6.74056e-13
2019-06-29			2⁵³	2⁵⁴	12240770277752593	53.443	17	2.56138e-8	237,129	5.48379e-8
TF systematically completed to 64 but no per-exponent detailed record exists
2022-12-25	slaur	palvi2-rtx	2⁶⁸	2⁷¹		-	-	0.104	-	-

ECM factoring results:
No ECM results for M4015431631

Lucas-Lehmer results:
No L-L results for M4015431631

PRP results:
No PRP results for M4015431631

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

TF factor-bounds graph:

2⁷¹

2⁵⁴

2³⁸

this exponent TF target: 92

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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