M6 979 871 Mersenne number exponent details

≡

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	137.0131	68.0556%	10000000	28985646690	502.3076	13.6835%	639.3206	72.4267%
Target	2⁶⁷	4.2571	65.6716%	45000	900000	0.0290	2.2395%	4.2860	66.4404%
Difference	+5	+132.7560	+2.3839%	+9955000	+28984746690	+502.2786	+11.4440%	+635.0346	+5.9863%

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	-	-	0.235%
2011-09-07	Carsten Kossendey	mother	445000	13683750		-		-	-	0.369	-	-	3.534%
2021-12-06	Seth_Tr	Manual testing	2000000	2000000		-		-	-	0.632	-	-	2.397%
2022-09-30	Jayder	Black_Adder	10000000	28985646690		-		-	-	502.3	-	-	13.684%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-10-25	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.088	-	-
2005-08-16	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.229	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.281	-	-
2014-02-15	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.535	-	-
2015-07-03	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.071	-	-
2016-04-26	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.141	-	-
2018-02-27	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.282	-	-
2020-04-10	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.565	-	-
2021-08-09	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.13	-	-
2021-09-07	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.26	-	-
2021-10-10	SRBase	Manual testing	2⁷¹	2⁷²		-	-	68.52	-	-

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
2012-09-08	ATH	quad	50000	5000000						3	0.995
2017-05-10	Sebastian Hornbostel	NZXT	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-26	ANONYMOUS	v4_computers	44433D2E43EBB4__	1.522
1999-07-27	ANONYMOUS	v4_computers	CF3CDA612C8E10BB	1.522
2002-01-08	ANONYMOUS	v4_computers	CF3CDA612C8E10BB	1.522

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 = 10000000, B2 = 28985646690 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

B1 = 2000000 (P-1 stage 1)

B1 = 445000, B2 = 13683750 (P-1 stage 2)

B1 = 445000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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