M4 005 356 371 Mersenne number exponent details

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is 2 ^4005356371 - 1

has 1205732411 decimal digits

takes 1,004,862.323 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	250,408.2189	65.2174%	20000000	9600000000	197,146.2306	4.2365%	447,554.4494	66.6910%
Difference	-21	-250,408.0995	-10.2878%	-20000000	-9600000000	-197,146.2306	-4.2365%	-447,554.3301	-11.7614%

Known prime factors (2 factors, 94.3 bits, 0.00000235% 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
4005356371	232310669519	12	37.757	29 29	2012-08-20	1	29	4.887e-12	0.0009	0.0009
4005356371	102763313582583113	18	56.512	12828236 2² × 331 × 9689	2019-10-16	331	9689	3.401e-6	0.3059	0.3585

1 Composite Factors:

P-1 results:
No P-1 results for M4005356371

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2019-06-28			2³⁷	2³⁸	232310669519	37.757	12	3.15632e-13	236,613	6.75976e-13
2019-10-16			2⁵⁶	2⁵⁷	102763313582583113	56.512	18	1.00431e-6	236,613	2.15088e-6
TF systematically completed to 64 but no per-exponent detailed record exists
2022-12-15	slaur	palvi2-rtx	2⁶⁸	2⁷¹		-	-	0.104	-	-

ECM factoring results:
No ECM results for M4005356371

Lucas-Lehmer results:
No L-L results for M4005356371

PRP results:
No PRP results for M4005356371

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

10³

10⁰

10¹

10²

10³

10⁴

TF factor-bounds graph:

2⁷¹

2⁵⁷

2³⁸

this exponent TF target: 92

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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