M6 957 527 Mersenne number exponent details

≡

is 2 ^6957527 - 1

has 2094425 decimal digits

takes 1.517 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

factored, 0 LL tests remaining

	Residue	Status
L-L	3F09E524797D48AA	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	4.2708	65.6716%	130000	2827500	0.0876	3.5784%	4.3583	66.9001%
Target	2⁶⁷	4.2708	65.6716%	45000	900000	0.0290	2.2383%	4.2997	66.4400%
Difference	-	-	-	+85000	+1927500	+0.0586	+1.3401%	+0.0586	+0.4600%

Known prime factors (1 factor, 69.8 bits, 0.00100291% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6957527	1012161053910619456967	22	69.778	72738564572629 83 × 613 × 4987 × 286673	2011-12-08	4987	286673	17.565	0.0064	0.0092

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-09-10	ANONYMOUS	v4_computers	30000	232500		-		-	-	0.013	-	-	1.387%
2011-12-08	James Heinrich	Q6600	130000	2827500			1012161053910619456967	22	69.778	0.088	3.034	0.175	3.578%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-21	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.044	-	-
1998-07-29	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-
2005-07-17	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.229	-	-

ECM factoring results:
No ECM results for M6957527

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-26	ANONYMOUS	v4_computers	3F09E524797D48AA	1.517
2001-10-25	ANONYMOUS	v4_computers	3F09E524797D48AA	1.517

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-01-22

Netanias

Win10

1012161053910619456967

824C5964E29EA6__

no

2019-02-10

kkmrkkblmbrbk

c5.large

1012161053910619456967

824C5964E29EA6B5

no

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

B1 = 130000, B2 = 2827500 (P-1 stage 2)

B1 = 130000 (P-1 stage 1)

B1 = 30000, B2 = 232500 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

TF factor-bounds graph:

2⁶³

2⁶²

2⁶¹

this exponent TF target: 67

TF double-checked to: 67.8

2⁵⁰

2⁶⁰

2⁷⁰

Last modified: 2023-04-26T21:34:10+00:00