M6 928 409 Mersenne number exponent details

≡

is 2 ^6928409 - 1

has 2085659 decimal digits

takes 1.511 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

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	2⁶⁷	4.2887	65.6716%	-	-	-	-	4.2887	65.6716%
Target	2⁶⁷	4.2887	65.6716%	45000	900000	0.0290	2.2367%	4.3177	66.4395%
Difference	-	-	-	-45000	-900000	-0.0290	-2.2367%	-0.0290	-0.7678%

Known prime factors (2 factors, 68.1 bits, 0.00098343% 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
6928409	831409081	9	29.631	60 2² × 3 × 5	-	4	5	1.046e-11	1.282e-6	2.574e-6
6928409	390194138063	12	38.505	28159 29 × 971	2008-09-08	29	971	5.788e-9	2.540e-5	3.138e-5

1 Composite Factors:

P-1 results:
No P-1 results for M6928409

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-08	Will Edgington	Manual testing	?	?	390194138063	38.505	12	5.02218e-10	7.339	2.43973e-9

ECM factoring results:
No ECM results for M6928409

Lucas-Lehmer results:
No L-L results for M6928409

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-01-19

ATH

ec2-1xd

831409081

390194138063

FD5FE587154709__

no

2019-01-27

kkmrkkblmbrbk

c5.large

831409081

390194138063

FD5FE587154709A2

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

10⁰

10¹

10²

10⁰

10¹

10²

10³

TF factor-bounds graph:

2

this exponent TF target: 67

TF double-checked to: 67.8

2⁵⁰

2⁶⁰

2⁷⁰

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