M7852241 Mersenne number exponent details

≡

is 2 ^7852241 - 1

has 2363761 decimal digits

takes 1.797 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 L-L tests remaining

	Residue	Status
L-L	B6D73DBFD4DCB8DB	double-checked
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	2⁶⁷	3.7841	65.6716%	1000000	1000000	0.3318	3.2062%	4.1159	66.7723%	3.2802%
PrimeNet	2⁶³	0.2033	63.4921%	34000	900000	0.0269	3.5557%	0.2302	64.7902%	1.2981%
GPU72	2⁶⁷	3.7841	65.6716%	55000	1200000	0.0389	2.5592%	3.8231	66.5502%	0.8785%
Difference	-	-	-	+945000	-200000	+0.2928	+0.6470%	+0.2928	+0.2221%	+0.2221%

Known prime factors (2 factors, 127.6 bits, 0.00162537% 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
7852241	12636032572020488377	20	63.454	804613139868 2² × 3 × 1049 × 1229 × 52009	2012-09-05	1229	52009	0.2740	0.0013	0.0018
7852241	20803311806894291761	20	64.173	1324673542680 2³ × 3 × 5 × 37 × 4597 × 64901	2012-09-05	4597	64901	0.4718	0.0026	0.0031

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
7852241	12636032572020488377 20803311806894291761	262871325597814670948015440740747361897	39	127.628

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-05-11T00:00:00	ANONYMOUS	v4_computers	40000	510000		-		-	-	0.022	-	-	1.916%
2012-09-05T08:37:00	nextPrime	alpha_277	1000000	1000000			12636032572020488377 20803311806894291761	39	127.628	0.332	3.593	0.664	3.206%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-08-09T00:00:00	ANONYMOUS	v4_computers	?	2⁶¹		-	-	0.020	-	-
1998-09-06T00:00:00	ANONYMOUS	v4_computers	?	2⁶²		-	-	0.039	-	-
1998-11-21T00:00:00	ANONYMOUS	v4_computers	?	2⁶³		-	-	0.125	-	-

ECM factoring results:
Exponent "7852241" not found

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-09-22T00:00:00	ANONYMOUS	v4_computers	B6D73DBFD4DCB8DB	1.797
2002-05-18T00:00:00	ANONYMOUS	v4_computers	B6D73DBFD4DCB8DB	1.797

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-03-29T13:32:11

kkmrkkblmbrbk

c5.xlarge

12636032572020488377

20803311806894291761

8A1132B2BADB1E__

no

2019-10-25T07:17:29

ATH

ec2-PRPCFDC

12636032572020488377

20803311806894291761

8A1132B2BADB1E2F

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 = 1000000 (P-1 stage 1)

B1 = 40000, B2 = 510000 (P-1 stage 2)

B1 = 40000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

TF factor-bounds graph:

2⁶⁷

2⁶³

2⁶²

2⁶¹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2019-10-25T07:17:29+00:00