M6 994 997 Mersenne number exponent details

≡

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	136.7168	68.0556%	2000000	258626550	5.0531	6.9847%	141.7699	70.2868%
Target	2⁶⁷	4.2479	65.6716%	45000	900000	0.0290	2.2403%	4.2768	66.4407%
Difference	+5	+132.4689	+2.3839%	+1955000	+257726550	+5.0242	+4.7444%	+137.4931	+3.8461%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6994997	87339947102858436187321	23	76.209	6243029632668780 2² × 3² × 5 × 7 × 43 × 1451 × 79412521	2021-12-06	1451	79412521	2,784.5	1.3684	2.5550

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-09-22	mkroska	v4_computers	30000	30000		-		-	-	0.009	-	-	0.235%
2011-09-08	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			87339947102858436187321	23	76.209	5.053	3.051	10.11	6.985%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-21	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-
2001-12-08	ANONYMOUS	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		-	-	1.068	-	-
2016-04-28	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.137	-	-
2018-02-26	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.273	-	-
2020-04-03	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.546	-	-
2020-07-26	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.09	-	-
2020-09-20	takahashi	Manual testing	2⁷⁰	2⁷¹		-	-	34.19	-	-
2021-09-26	SRBase	Manual testing	2⁷¹	2⁷²		-	-	68.37	-	-

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
2012-09-21	Arne Kleppestrand	Arne	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)
1999-07-04	ANONYMOUS	v4_computers	98042A820DACD809	1.525
2001-11-14	mkroska	v4_computers	3AEDDE96EE673D93	1.525
2002-01-08	ANONYMOUS	v4_computers	3AEDDE96EE673D93	1.525

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 = 30000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

this exponent TF target: 67

TF double-checked to: 67.7

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

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

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