M4 031 048 027 Mersenne number exponent details

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is 2 ^4031048027 - 1

has 1213466371 decimal digits

takes 1,011,307.836 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	0.1186	54.9296%	-	-	-	-	0.1186	54.9296%
Target	2⁹²	248,812.2563	65.2174%	20000000	9600000000	197,146.2306	4.2391%	445,958.4869	66.6919%
Difference	-21	-248,812.1377	-10.2878%	-20000000	-9600000000	-197,146.2306	-4.2391%	-445,958.3683	-11.7623%

Known prime factors (2 factors, 94.5 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
4031048027	902954758049	12	39.716	112 2⁴ × 7	2012-08-20	16	16	2.301e-11	0.0058	0.0118
4031048027	31983560484818209	17	54.828	3967152 2⁴ × 3 × 7 × 11807	2019-06-30	16	11807	9.525e-7	0.2395	0.4369

1 Composite Factors:

P-1 results:
No P-1 results for M4031048027

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2019-06-30			2³⁹	2⁴⁰	902954758049	39.716	12	4.84489e-12	237,930	1.03674e-11
2019-06-30			2⁵⁴	2⁵⁵	31983560484818209	54.828	17	3.57204e-7	237,930	7.64367e-7
TF systematically completed to 64 but no per-exponent detailed record exists
2023-01-07	slaur	palvi2-rtx	2⁶⁸	2⁷¹		-	-	0.104	-	-

ECM factoring results:
No ECM results for M4031048027

Lucas-Lehmer results:
No L-L results for M4031048027

PRP results:
No PRP results for M4031048027

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

10⁴

10⁵

TF factor-bounds graph:

2⁷¹

2⁵⁵

2⁴⁰

this exponent TF target: 92

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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