M4 053 154 823 Mersenne number exponent details

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is 2 ^4053154823 - 1

has 1220121179 decimal digits

takes 1,016,853.981 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	0.1180	54.9296%	-	-	-	-	0.1180	54.9296%
Target	2⁹²	247,455.1796	65.2174%	20000000	9600000000	197,146.2306	4.2413%	444,601.4102	66.6926%
Difference	-21	-247,455.0617	-10.2878%	-20000000	-9600000000	-197,146.2306	-4.2413%	-444,601.2922	-11.7631%

Known prime factors (2 factors, 115.7 bits, 0.00000285% 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
4053154823	7071069053728633	16	52.651	872292 2² × 3 × 157 × 463	2013-12-28	157	463	2.791e-7	0.0632	0.1162
4053154823	9549549987203376919	19	63.050	1178039133 3⁴ × 251 × 57943	2013-12-28	251	57943	0.0004	1.2347	2.1448

1 Composite Factors:

P-1 results:
No P-1 results for M4053154823

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2019-07-01			2⁵²	2⁵³	7071069053728633	52.651	16	1.31106e-7	239,065	2.80350e-7
TF systematically completed to 64 but no per-exponent detailed record exists
2023-01-31	slaur	palvi2-rtx	2⁶⁸	2⁷¹		-	-	0.103	-	-

ECM factoring results:
No ECM results for M4053154823

Lucas-Lehmer results:
No L-L results for M4053154823

PRP results:
No PRP results for M4053154823

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

10¹

10²

10³

10¹

10²

10³

10⁴

10⁵

TF factor-bounds graph:

2⁷¹

2⁵³

this exponent TF target: 92

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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