M13 770 461 Mersenne number exponent details

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M13770461

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is 2 ^13770461 - 1

has 4145322 decimal digits

takes 6.110 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	4F640459FCCA4833	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷³	138.9092	67.1233%	1600000	1604717400	57.2198	8.4883%	196.1291	69.9140%
Target	2⁶⁹	8.6698	65.2174%	90000	11000000	0.4403	2.7907%	9.1101	66.1881%
Difference	+4	+130.2395	+1.9059%	+1510000	+1593717400	+56.7795	+5.6976%	+187.0190	+3.7259%

Known prime factors:
No known factors for M13770461

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-07-02	dave_0273	v4_computers	80000	1420000		-		-	-	0.098	-	-	1.497%
2015-06-28	Sid & Andy	Speck	155000	2983750		-		-	-	0.199	-	-	2.087%
2023-03-19	nordi	sweet16_30.8b14	1600000	1600000		-		-	-	1.029	-	-	2.174%
2023-07-27	nordi	sweet16_30.8b14	1600000	1604717400		-		-	-	57.22	-	-	8.488%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-10-15	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.258	-	-
2001-03-05	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.258	-	-
2001-04-21	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.258	-	-
2000-10-22	Ed Straker	v4_computers	2¹	2⁶⁵		-	-	0.530	-	-
2014-07-02	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.543	-	-
2015-08-19	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	1.085	-	-
2017-12-23	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	2.171	-	-
2018-01-14	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	4.341	-	-
2021-08-08	SRBase	Manual testing	2⁶⁹	2⁷⁰		-	-	8.683	-	-
2021-09-05	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	17.37	-	-
2021-10-01	Jon Pace	Manual testing	2⁷¹	2⁷²		-	-	34.73	-	-
2023-10-28	Naegi Makoto	GPU72_TF	2⁷²	2⁷³		-	-	69.46	-	-

ECM factoring results:

Total ECM effort:	0.675 GHz-days
Estimated T-Level:	0.192

Digits	B1	Complete	FacMiss
20	11000	0.038	96.227%
25	50000	0.004	99.645%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		1	0.675

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-08-04	Tom Bammann	Work	50000	5000000						1	0.675

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	acterAG	5	5FA2E4C032E19DBA	6.110
2005-02-12	Sturle Sunde	v4_computers	4F640459FCCA4833	6.110
2005-04-26	ANONYMOUS	v4_computers	4F640459FCCA4833	6.110

PRP results:
No PRP results for M13770461

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 = 1600000, B2 = 1604717400 (P-1 stage 2)

B1 = 1600000 (P-1 stage 1)

B1 = 155000, B2 = 2983750 (P-1 stage 2)

B1 = 155000 (P-1 stage 1)

B1 = 80000, B2 = 1420000 (P-1 stage 2)

B1 = 80000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

this exponent TF target: 69

TF double-checked to: 67.9

ECM T-Level=0.19 ~= -16-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

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Last modified: 2023-10-28T02:07:01+00:00

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
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0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront