M3 041 Mersenne number exponent details

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is 2 ³⁰⁴¹ - 1

has 916 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

0 primality tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
PRP	-unknown-	-unknown-
Cofactor is a certified prime

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	9,771.1008	82.0896%	-	-	-	-	9,771.1008	82.0896%
Target	2⁴⁴	0.0008	72.7273%	500	50000	0.0000	0.8701%	0.0008	72.9646%
Difference	+23	+9,771.1000	+9.3623%	-500	-50000	0.0000	-0.8701%	+9,771.1000	+9.1250%

Known prime factors (3 factors, 3,041.0 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
3041	24329	5	14.570	4 2²	-	4	4	7.183e-13	2.392e-10	4.869e-10
3041	5565031	7	22.408	915 3 × 5 × 61	2009-03-05	5	61	2.201e-10	4.816e-10	6.086e-10
3041	hide decimal representation P905 click to show decimal representation	905	3,004.022		2009-03-05

1 Composite Factors:

P-1 results:
No P-1 results for M3041

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-03-05	ANONYMOUS	Manual testing	?	?	5565031	22.408	7	3.63904e-11	0.001	2.23660e-7

ECM factoring results:
No ECM results for M3041

Lucas-Lehmer results:
No L-L results for M3041

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-09

kkmrkkblmbrbk

c4.large

24329

5565031

PRP

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

10⁰

10¹

10²

TF factor-bounds graph:

2

this exponent TF target: 44

TF double-checked to: 67.9

2⁵⁰

2⁶⁰

2⁷⁰

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