M6 919 687 Mersenne number exponent details

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	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷²	138.2048	68.0556%	4000000	414323910	8.3331	7.9713%	146.5379	70.6019%
Target	2⁶⁷	4.2941	65.6716%	45000	900000	0.0290	2.2363%	4.3231	66.4393%
Difference	+5	+133.9106	+2.3839%	+3955000	+413423910	+8.3042	+5.7350%	+142.2148	+4.1626%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-08-31	ANONYMOUS	v4_computers	30000	232500		-		-	-	0.013	-	-	0.669%
2011-11-22	James Heinrich	i7-920	130000	2665000		-		-	-	0.085	-	-	1.986%
2020-01-11	takahashi	vaio	600000	12000000	12	-		-	-	0.386	-	-	3.581%
2021-11-24	Seth_Tr	Manual testing	4000000	110000000	12	-		-	-	3.091	-	-	6.531%
2021-12-02	Seth_Tr	Manual testing	4000000	414323910		-		-	-	8.333	-	-	7.971%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-10-18	Martin Fuchs	v4_computers	2¹	2⁶²		-	-	0.089	-	-
2004-03-16	Sturle Sunde	v4_computers	2¹	2⁶³		-	-	0.231	-	-
2014-02-09	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.284	-	-
2014-02-17	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.540	-	-
2015-06-26	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.080	-	-
2016-04-02	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.160	-	-
2018-02-27	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	4.320	-	-
2020-05-15	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.639	-	-
2021-07-18	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	17.28	-	-
2021-08-11	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	34.56	-	-
2021-09-25	SRBase	Manual testing	2⁷¹	2⁷²		-	-	69.12	-	-

ECM factoring results:

Total ECM effort:	2.984 GHz-days
Estimated T-Level:	1.731

Digits	B1	Complete	FacMiss
20	11000	0.346	70.740%
25	50000	0.032	96.848%
30	250000	0.002	99.798%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	2.984

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-08-17	Christopher Tompkins	iMac2	50000	5000000						3	0.995
2017-04-04	Yxinity	Elena	50000	5000000						3	0.995
2017-04-07	Yxinity	Manual testing	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-07-12	ANONYMOUS	v4_computers	1B07AA8D614ABAFB	1.509
2001-09-30	ANONYMOUS	v4_computers	1B07AA8D614ABAFB	1.509

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 = 4000000, B2 = 414323910 (P-1 stage 2)

B1 = 4000000, B2 = 110000000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 600000, B2 = 12000000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 130000, B2 = 2665000 (P-1 stage 2)

B1 = 130000 (P-1 stage 1)

B1 = 30000, B2 = 232500 (P-1 stage 2)

B1 = 30000 (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

this exponent TF target: 67

TF double-checked to: 67.7

ECM T-Level=1.73 ~= -11-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