M4 004 213 141 Mersenne number exponent details

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is 2 ^4004213141 - 1

has 1205388265 decimal digits

takes 1,004,575.510 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	250,479.7121	65.2174%	20000000	6000000000	125,796.0639	4.2364%	376,275.7760	66.6909%
Difference	-21	-250,479.5927	-10.2878%	-20000000	-6000000000	-125,796.0639	-4.2364%	-376,275.6566	-11.7613%

Known prime factors (1 factor, 34.5 bits, 0.00000086% 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
4004213141	24025278847	11	34.484	3 3	2012-08-20	1	3	5.756e-13	0.0004	0.0007

P-1 results:
No P-1 results for M4004213141

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2019-06-28			2³⁴	2³⁵	24025278847	34.484	11	4.08261e-15	236,554	8.74389e-15
2022-12-14	slaur	palvi2-rtx	2⁶⁸	2⁷¹		-	-	0.105	-	-

ECM factoring results:
No ECM results for M4004213141

Lucas-Lehmer results:
No L-L results for M4004213141

PRP results:
No PRP results for M4004213141

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

TF factor-bounds graph:

2⁷¹

2³⁵

this exponent TF target: 92

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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