M4 008 312 211 Mersenne number exponent details

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is 2 ^4008312211 - 1

has 1206622208 decimal digits

takes 1,005,603.883 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	0.1193	54.9296%	-	-	-	-	0.1193	54.9296%
Target	2⁹²	250,223.5610	65.2174%	20000000	9600000000	197,146.2306	4.2368%	447,369.7915	66.6911%
Difference	-21	-250,223.4417	-10.2878%	-20000000	-9600000000	-197,146.2306	-4.2368%	-447,369.6722	-11.7615%

Known prime factors (3 factors, 128.0 bits, 0.00000319% 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
4008312211	232482108239	12	37.758	29 29	2012-08-20	1	29	4.883e-12	0.0009	0.0009
4008312211	448930967633	12	38.708	56 2³ × 7	2019-06-28	8	8	1.035e-11	0.0029	0.0059
4008312211	3288748019505703	16	51.546	410241 3 × 13 × 67 × 157	2019-06-28	67	157	1.320e-7	0.0262	0.0496

4 Composite Factors:

P-1 results:
No P-1 results for M4008312211

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2019-06-28			2³⁷	2³⁸	232482108239	37.758	12	3.15399e-13	236,764	6.75411e-13
2019-06-28			2³⁸	2³⁹	448930967633	38.708	12	1.21809e-12	236,764	2.60849e-12
2019-06-28			2⁵¹	2⁵²	3288748019505703	51.546	16	5.71989e-8	236,764	1.22489e-7
TF systematically completed to 64 but no per-exponent detailed record exists
2022-12-18	slaur	palvi2-rtx	2⁶⁸	2⁷¹		-	-	0.104	-	-

ECM factoring results:
No ECM results for M4008312211

Lucas-Lehmer results:
No L-L results for M4008312211

PRP results:
No PRP results for M4008312211

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

TF factor-bounds graph:

2⁷¹

2⁵²

2³⁹

2³⁸

this exponent TF target: 92

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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