M409 Mersenne number exponent details

≡

is 2 ⁴⁰⁹ - 1

has 124 decimal digits

takes 0.000 GHz-days to do one PRP test

Has been fully factored.

Last-known PrimeNet details:

Exponent is not assigned to anyone

factored, 0 PRP tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
PRP	7AE1248CF73FF893	PRP-tested
Cofactor is a certified prime

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	unknown			-	-	-	-	0.0000	0.0000%
Target	2⁴⁴	0.0057	79.5455%	500	50000	0.0000	0.4482%	0.0057	79.6371%
Difference	-44	-0.0057	-79.5455%	-500	-50000	0.0000	-0.4482%	-0.0057	-79.6371%

Known prime factors (3 factors, 409.0 bits, 100.00000000% known):

Remaining cofactor is a certified-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
409	4480666067023	13	42.027	5477586879 3 × 337 × 5417989	-	337	5417989	0.0027	4.356e-6	8.127e-6
409	76025626689833	14	46.112	92940863924 2² × 233 × 99721957	-	233	99721957	0.0255	8.010e-5	0.0001
409	hide decimal representation P97 click to show decimal representation	97	320.862

1 Composite Factors:

P-1 results:
No P-1 results for M409

Trial Factoring results:
No TF results for M409

ECM factoring results:
No ECM results for M409

Lucas-Lehmer results:
No L-L results for M409

PRP results:

date	userid	compid	cofactors	res64	PRP
2018-01-24	Luke_Richards	work-laptop		7AE1248CF73FF893	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

10¹

10²

10³

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.9

2⁵⁰

JSON version of this page

Last modified: 2023-10-02T12:12:48+00:00