M6 944 429 Mersenne number exponent details

≡

is 2 ^6944429 - 1

has 2090482 decimal digits

takes 1.514 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	0EAB429A9CFC4B89	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	4.2788	65.6716%	445000	13350000	0.3630	5.7414%	4.6418	67.6426%
Target	2⁶⁷	4.2788	65.6716%	45000	7200000	0.1375	2.2376%	4.4163	66.4398%
Difference	-	-	-	+400000	+6150000	+0.2255	+3.5038%	+0.2255	+1.2028%

Known prime factors (1 factor, 71.2 bits, 0.00102559% 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
6944429	2752167233265849371849	22	71.221	198156481495156 2² × 41 × 971 × 1979 × 628781	2011-09-04	1979	628781	112.91	0.0114	0.0202

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	30000		-		-	-	0.009	-	-	0.537%
2011-09-04	Carsten Kossendey	mother	445000	13350000			2752167233265849371849	22	71.221	0.363	3.029	0.726	5.741%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-05	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-
2005-03-20	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.230	-	-

ECM factoring results:
No ECM results for M6944429

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-26	ANONYMOUS	v4_computers	0EAB429A9CFC4B89	1.514
2001-09-22	ANONYMOUS	v4_computers	0EAB429A9CFC4B89	1.514

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-01-21

ATH

ec2-1xd

2752167233265849371849

0E2122B8D0116D__

no

2019-02-05

kkmrkkblmbrbk

c5.large

2752167233265849371849

0E2122B8D0116D08

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 = 445000, B2 = 13350000 (P-1 stage 2)

B1 = 445000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶³

2⁶²

this exponent TF target: 67

TF double-checked to: 67.8

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

Last modified: 2023-06-05T21:50:05+00:00