M6 968 561 Mersenne number exponent details

≡

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	137.2355	68.0556%	3000000	75000000	2.1888	5.9859%	139.4243	69.9677%
Target	2⁶⁷	4.2640	65.6716%	45000	900000	0.0290	2.2389%	4.2930	66.4402%
Difference	+5	+132.9715	+2.3839%	+2955000	+74100000	+2.1599	+3.7470%	+135.1313	+3.5275%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-12-22	ANONYMOUS	v4_computers	30000	30000		-		-	-	0.009	-	-	0.234%
2011-05-01	Carsten Kossendey	leela	440000	13530000		-		-	-	0.365	-	-	3.519%
2021-11-09	Seth_Tr	Manual testing	3000000	75000000	12	-		-	-	2.189	-	-	5.986%

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	-	-
2005-08-01	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.229	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.282	-	-
2014-02-15	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.536	-	-
2015-06-26	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.072	-	-
2016-04-25	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.145	-	-
2018-02-27	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.289	-	-
2020-04-24	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.579	-	-
2021-08-07	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.16	-	-
2021-09-08	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.32	-	-
2021-09-28	SRBase	Manual testing	2⁷¹	2⁷²		-	-	68.63	-	-

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
2012-09-16	LaurV	bc1	50000	5000000						3	0.995
2017-07-02	Oliver Kruse	ECM-HTC	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-15	ANONYMOUS	v4_computers	3C24ECDE9873F557	1.520
2001-12-22	ANONYMOUS	v4_computers	3C24ECDE9873F557	1.520

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

B1 = 3000000 (P-1 stage 1)

B1 = 440000, B2 = 13530000 (P-1 stage 2)

B1 = 440000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

this exponent TF target: 67

TF double-checked to: 67.8

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