M697910431 Mersenne number exponent details

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M697910431

<<<

is 2 ^697910431 - 1

has 210091975 decimal digits

takes 22,625.545 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- 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	Prob over default TF
Actual	2⁷³	2.7408	58.9041%	-	-	-	-	2.7408	58.9041%	0.0000%
PrimeNet	2⁸⁰	350.8567	62.5000%	2600000	180000000	576.5586	5.6319%	927.4153	64.6120%	2.1120%
GPU72	2⁸⁴	5,613.7112	64.2857%	4000000	180000000	638.7836	4.2188%	6,252.4948	65.7924%	1.5067%
Difference	-11	-5,610.9704	-5.3816%	-4000000	-180000000	-638.7836	-4.2188%	-6,249.7540	-6.8883%	-6.8883%

Known prime factors (2 factors, 134.8 bits, 0.00001931% 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
697910431	60676366253591735593	20	65.718	43470023916 2² × 3 × 11² × 31² × 31153	2013-11-13	961	31153	0.0114	0.1225	0.1490
697910431	614881825148280845641	21	69.059	440516288220 2² × 3 × 5 × 7341938137	2022-08-13	5	7341938137	0.3313	18,803	35,120

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
697910431	60676366253591735593 614881825148280845641	37308794825374042084846914832298918600113	41	134.777

P-1 results:
No P-1 results for M697910431

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2010-01-04T00:00:00	linded	v4_computers	2⁶¹	2⁶²		-	-	0.000	-	-
2010-06-26T23:50:00	Architects Cubed	m1_53	2⁶³	2⁶⁴		-	-	0.003	-	-
2012-01-25T15:56:00	lalera	Manual testing	2⁶⁴	2⁶⁵		-	-	0.005	-	-
2013-11-13T23:22:00	sasaki	Manual testing	2⁶⁵	2⁶⁶	60676366253591735593	65.718	20	0.001	46,365	0.002
2022-08-13T01:07:43	LordJulius	Manual testing	2¹	2⁷⁰	60676366253591735593	65.718	20	0.011	46,365	0.023
2022-08-13T01:07:43	LordJulius	Manual testing	2¹	2⁷⁰	614881825148280845641	69.059	21	0.331	46,365	0.679
2022-08-13T01:07:43	LordJulius	Manual testing	2⁷⁰	2⁷¹		-	-	0.343	-	-
2022-08-13T01:07:43	LordJulius	Manual testing	2⁷¹	2⁷²		-	-	0.685	-	-
2022-08-13T01:07:43	LordJulius	Manual testing	2⁷²	2⁷³		-	-	1.371	-	-

ECM factoring results:
No ECM results for M697910431

Lucas-Lehmer results:
No L-L results for M697910431

PRP results:
No PRP results for M697910431

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

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁶

2⁶⁵

2⁶⁴

2⁶²

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-08-13T01:07:43+00:00

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront