M4 000 351 961 Mersenne number exponent details

≡

is 2 ^4000351961 - 1

has 1204225934 decimal digits

takes 1,003,606.818 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	250,721.4777	65.2174%	20000000	6000000000	125,796.0639	4.2360%	376,517.5416	66.6908%
Difference	-21	-250,721.3582	-10.2878%	-20000000	-6000000000	-125,796.0639	-4.2360%	-376,517.4220	-11.7612%

Known prime factors (1 factor, 47.6 bits, 0.00000119% 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
4000351961	208010301268079	15	47.564	25999 25999	2012-12-18	1	25999	8.916e-9	0.5156	0.9624

P-1 results:
No P-1 results for M4000351961

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2019-06-28			2⁴⁷	2⁴⁸	208010301268079	47.564	15	4.22927e-9	236,356	9.05914e-9
2022-12-10	slaur	palvi2-rtx	2⁶⁸	2⁷¹		-	-	0.105	-	-

ECM factoring results:
No ECM results for M4000351961

Lucas-Lehmer results:
No L-L results for M4000351961

PRP results:
No PRP results for M4000351961

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

TF factor-bounds graph:

2⁷¹

2⁴⁸

this exponent TF target: 92

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

JSON version of this page

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