M4 000 351 997 Mersenne number exponent details

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is 2 ^4000351997 - 1

has 1204225945 decimal digits

takes 1,003,606.827 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	2⁷²	0.2391	55.5556%	-	-	-	-	0.2391	55.5556%
Target	2⁹²	250,721.4754	65.2174%	20000000	6000000000	125,796.0639	4.2360%	376,517.5393	66.6908%
Difference	-20	-250,721.2363	-9.6618%	-20000000	-6000000000	-125,796.0639	-4.2360%	-376,517.3002	-11.1352%

Known prime factors (1 factor, 71.4 bits, 0.00000179% 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
4000351997	3189510910094977016833	22	71.434	398653782528 2⁹ × 3 × 227 × 271 × 4219	2020-07-08	512	4219	0.2015	0.2597	0.3791

P-1 results:
No P-1 results for M4000351997

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2020-07-08	ViliamF	3GPU	2⁷¹	2⁷²	3189510910094977016833	71.434	22	0.120	220,686	0.256

ECM factoring results:
No ECM results for M4000351997

Lucas-Lehmer results:
No L-L results for M4000351997

PRP results:
No PRP results for M4000351997

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

10¹

10²

10³

10¹

10²

10³

10⁴

TF factor-bounds graph:

2⁷²

this exponent TF target: 92

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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Last modified: 2023-10-02T12:12:48+00:00