M4 031 697 353 Mersenne number exponent details

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is 2 ^4031697353 - 1

has 1213661837 decimal digits

takes 1,011,470.739 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	248,772.1838	65.2174%	20000000	9600000000	197,146.2306	4.2392%	445,918.4143	66.6919%
Difference	-21	-248,772.0652	-10.2878%	-20000000	-9600000000	-197,146.2306	-4.2392%	-445,918.2958	-11.7623%

Known prime factors (2 factors, 99.0 bits, 0.00000245% 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
4031697353	903100207073	12	39.716	112 2⁴ × 7	2012-08-20	16	16	2.301e-11	0.0058	0.0118
4031697353	686984102300844457	18	59.253	85197876 2² × 3 × 7099823	2020-01-05	4	7099823	2.068e-5	140.72	262.82

1 Composite Factors:

P-1 results:
No P-1 results for M4031697353

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2019-06-30			2³⁹	2⁴⁰	903100207073	39.716	12	4.84411e-12	237,964	1.03655e-11
2020-01-05	slaur	palvi2-rtx	2¹	2⁶⁴	686984102300844457	59.253	18	0.001	222,415	0.002
Missing TF 64 - 65
Missing TF 65 - 66
Missing TF 66 - 67
Missing TF 67 - 68
2023-01-07	slaur	palvi2-rtx	2⁶⁸	2⁷¹		-	-	0.104	-	-

ECM factoring results:
No ECM results for M4031697353

Lucas-Lehmer results:
No L-L results for M4031697353

PRP results:
No PRP results for M4031697353

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

10⁶

10⁷

TF factor-bounds graph:

2⁷¹

2⁶⁴

2⁴⁰

this exponent TF target: 92

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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