M4 008 312 221 Mersenne number exponent details

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is 2 ^4008312221 - 1

has 1206622211 decimal digits

takes 1,005,603.885 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	2⁷³	0.4772	56.1644%	-	-	-	-	0.4772	56.1644%
Target	2⁹²	250,223.5603	65.2174%	20000000	6000000000	125,796.0639	4.2368%	376,019.6242	66.6911%
Difference	-19	-250,223.0831	-9.0530%	-20000000	-6000000000	-125,796.0639	-4.2368%	-376,019.1470	-10.5267%

Known prime factors (1 factor, 72.9 bits, 0.00000182% 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
4008312221	8673621344154546962423	22	72.877	1081954307191 23 × 47041491617	2021-04-26	23	47041491617	0.4267	932,338	1,741,349

P-1 results:
No P-1 results for M4008312221

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2021-04-26	ramgeis	r4mg31s	2⁷²	2⁷³	8673621344154546962423	72.877	22	0.239	2,044,540	0.489

ECM factoring results:
No ECM results for M4008312221

Lucas-Lehmer results:
No L-L results for M4008312221

PRP results:
No PRP results for M4008312221

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

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10⁴

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10¹¹

TF factor-bounds graph:

2⁷³

this exponent TF target: 92

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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