M1 429 414 781 Mersenne number exponent details

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is 2 ^1429414781 - 1

has 430296726 decimal digits

takes 115,544.361 GHz-days to do one PRP test

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	2⁶⁸	0.0417	54.4118%	-	-	-	-	0.0417	54.4118%
Target	2⁸⁷	21,927.1149	64.3678%	8000000	2000000000	13,658.2467	4.3524%	35,585.3616	65.9187%
Difference	-19	-21,927.0732	-9.9561%	-8000000	-2000000000	-13,658.2467	-4.3524%	-35,585.3199	-11.5069%

Known prime factors (1 factor, 46.0 bits, 0.00000322% known):

Remaining cofactor is PRP status unknown

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1429414781	68654791931431	14	45.964	24015 3 × 5 × 1601	2012-12-22	5	1601	3.865e-9	0.0108	0.0191

P-1 results:
No P-1 results for M1429414781

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2019-06-29			2¹	2⁵⁵	68654791931431	45.964	14	3.35780e-6	234,530	0.093
2023-09-11	JamesHeinrich	RTX4090	2¹	2⁶⁸	68654791931431	45.964	14	0.042	234,530	0.093

ECM factoring results:
No ECM results for M1429414781

Lucas-Lehmer results:
No L-L results for M1429414781

PRP results:
No PRP results for M1429414781

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

10³

10⁴

TF factor-bounds graph:

2⁶⁸

2⁵⁵

this exponent TF target: 87

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

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