M6 993 667 Mersenne number exponent details

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M6993667

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is 2 ^6993667 - 1

has 2105304 decimal digits

takes 1.525 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	B4136ACA8FE9130E	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	136.7428	68.0556%	2000000	258626550	5.0531	6.9845%	141.7959	70.2867%
Target	2⁶⁷	4.2487	65.6716%	45000	900000	0.0290	2.2402%	4.2776	66.4407%
Difference	+5	+132.4941	+2.3839%	+1955000	+257726550	+5.0242	+4.7443%	+137.5183	+3.8461%

Known prime factors:
No known factors for M6993667

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-06-11	ANONYMOUS	v4_computers	90000	90000		-		-	-	0.028	-	-	0.524%
2011-09-09	Carsten Kossendey	mother	445000	13572500		-		-	-	0.367	-	-	3.529%
2021-11-09	Seth_Tr	Manual testing	3000000	75000000	12	-		-	-	2.189	-	-	5.988%
2021-12-06	Seth_Tr	Manual testing	2000000	258626550		-		-	-	5.053	-	-	6.985%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-05	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.044	-	-
1998-08-02	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-
1999-12-01	Mark Blanke	v4_computers	2¹	2⁶³		-	-	0.228	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.281	-	-
2014-02-14	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.534	-	-
2015-07-03	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.069	-	-
2016-04-28	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.137	-	-
2018-02-27	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.274	-	-
2020-04-03	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.548	-	-
2020-07-26	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.10	-	-
2020-09-16	takahashi	Manual testing	2⁷⁰	2⁷¹		-	-	34.19	-	-
2021-09-28	SRBase	Manual testing	2⁷¹	2⁷²		-	-	68.38	-	-

ECM factoring results:

Total ECM effort:	1.989 GHz-days
Estimated T-Level:	1.154

Digits	B1	Complete	FacMiss
20	11000	0.231	79.392%
25	50000	0.021	97.887%
30	250000	0.001	99.865%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	1.989

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-09-15	Clown_Royal	lab2	50000	5000000						3	0.995
2017-05-16	Benoit Germain	ANN-BGERMAIN	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2000-09-23	ANONYMOUS	v4_computers	B4136ACA8FE9130E	1.525
2002-05-11	ANONYMOUS	v4_computers	B4136ACA8FE9130E	1.525

PRP results:
No PRP results for M6993667

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 = 2000000, B2 = 258626550 (P-1 stage 2)

B1 = 3000000, B2 = 75000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 2000000 (P-1 stage 1)

B1 = 445000, B2 = 13572500 (P-1 stage 2)

B1 = 445000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

this exponent TF target: 67

TF double-checked to: 67.7

ECM T-Level=1.15 ~= -13-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

Last modified: 2023-03-23T17:39:31+00:00

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront