M20 489 611 Mersenne number exponent details

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is 2 ^20489611 - 1

has 6167988 decimal digits

takes 14.521 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	13BB06700386CB4B	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁸	2.9090	63.2353%	310000	310000	0.3186	2.0830%	3.2276	64.0011%
Target	2⁶⁹	5.8267	63.7681%	150000	4500000	0.3977	3.7711%	6.2244	65.1345%
Difference	-1	-2.9177	-0.5328%	+160000	-4190000	-0.0791	-1.6881%	-2.9968	-1.1334%

Known prime factors (1 factor, 66.8 bits, 0.00032608% 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
20489611	129583117728183271391	21	66.812	3162166371245 5 × 7 × 83 × 271 × 1433 × 2803	2015-02-27	1433	2803	1.0910	0.0015	0.0030

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	310000	310000		-	MISSED FACTOR!	-	-	0.319	-	-	2.083%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2002-10-07	ANONYMOUS	v4_computers	2¹	2⁶⁶		-	-	0.721	-	-
2003-01-25	ANONYMOUS	v4_computers	2¹	2⁶⁶		-	-	0.721	-	-
2003-02-02	ANONYMOUS	v4_computers	2¹	2⁶⁶		-	-	0.721	-	-
2015-02-27	NR	Manual testing	2⁶⁶	2⁶⁷*	129583117728183271391	66.812	21	0.370	33.82	0.862
2022-04-11	LordJulius	Manual testing	2⁶⁶	2⁶⁷	129583117728183271391	66.812	21	0.370	33.82	0.862
2022-04-11	LordJulius	Manual testing	2⁶⁷	2⁶⁸		-	-	1.459	-	-

ECM factoring results:
No ECM results for M20489611

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2004-11-22	ANONYMOUS	v4_computers	13BB06700386CB4B	14.52
2008-03-05	dariop2	v4_computers	13BB06700386CB4B	14.52

PRP results:
No PRP results for M20489611

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 = 310000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

this exponent TF target: 69

TF double-checked to: 67.7

2⁵⁰

2⁶⁰

2⁷⁰

Last modified: 2023-03-25T13:08:14+00:00