M21 055 513 Mersenne number exponent details

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is 2 ^21055513 - 1

has 6338341 decimal digits

takes 14.922 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	54B11218B2439607	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	1.4112	62.6866%	245000	4042500	0.4644	4.8774%	1.8756	64.5065%
Target	2⁶⁹	5.6701	63.7681%	150000	22500000	1.4054	3.7852%	7.0755	65.1396%
Difference	-2	-4.2589	-1.0815%	+95000	-18457500	-0.9411	+1.0921%	-5.1999	-0.6331%

Known prime factors (1 factor, 66.4 bits, 0.00031517% 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
21055513	94711434693770770399	20	66.360	2249088746823 3² × 43 × 83 × 191 × 366593	2015-04-09	191	366593	0.7480	0.0207	0.0383

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-13	ANONYMOUS	v4_computers	245000	4042500		-	MISSED FACTOR!	-	-	0.464	-	-	4.877%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-04-21	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.000	-	-
2002-11-02	ANONYMOUS	v4_computers	2¹	2⁶⁶		-	-	0.701	-	-
2015-04-09	NR	Manual testing	2⁶⁶	2⁶⁷*	94711434693770770399	66.360	20	0.047	34.50	0.108

ECM factoring results:
No ECM results for M21055513

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2005-05-12	Dusty	v4_computers	D43B884BDFF7E50B	14.92
2006-07-25	gangho	v4_computers	54B11218B2439607	14.92
2008-07-25	ANONYMOUS	v4_computers	54B11218B2439607	14.92

PRP results:
No PRP results for M21055513

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

B1 = 245000, B2 = 4042500 (P-1 stage 2)

B1 = 245000 (P-1 stage 1)

10¹

10²

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10⁷

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁵⁶

this exponent TF target: 69

TF double-checked to: 67.9

2⁵⁰

2⁶⁰

2⁷⁰

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