M6 998 209 Mersenne number exponent details

≡

is 2 ^6998209 - 1

has 2106671 decimal digits

takes 1.526 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	39D84802B6EC8D3F	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	4.2459	65.6716%	-	-	-	-	4.2459	65.6716%
Target	2⁶⁷	4.2459	65.6716%	45000	7200000	0.1375	2.2404%	4.3834	66.4407%
Difference	-	-	-	-45000	-7200000	-0.1375	-2.2404%	-0.1375	-0.7691%

Known prime factors (1 factor, 71.5 bits, 0.00102122% 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
6998209	3263332080056976190199	22	71.467	233154802897211 13 × 23 × 29 × 71 × 5903 × 64157	2001-12-22	5903	64157	103.09	0.0029	0.0038

P-1 results:
No P-1 results for M6998209

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-12-22	ANONYMOUS	v4_computers	?	?	3263332080056976190199	71.467	22	34.78	3.081	70.21
1998-07-05	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-

ECM factoring results:
No ECM results for M6998209

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-02	ANONYMOUS	v4_computers	39D84802B6EC8D3F	1.526

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-01-30

Oliver Kruse

GTX-6

3263332080056976190199

D357532AF1F6B9__

no

2019-02-22

kkmrkkblmbrbk

c5.large

3263332080056976190199

D357532AF1F6B950

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

10²

10³

10⁴

10²

10³

10⁴

10⁵

TF factor-bounds graph:

2⁶²

2

this exponent TF target: 67

TF double-checked to: 67.8

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

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