M2758531 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	21.6075	67.6471%	2700000	84000000	0.7984	7.6790%	22.4059	70.1315%	2.4844%
PrimeNet	2⁵⁹	0.0278	62.7119%	12000	220000	0.0026	2.8541%	0.0305	63.7761%	1.0642%
GPU72	2⁶³	0.5786	65.0794%	15000	240000	0.0031	1.7449%	0.5816	65.6887%	0.6093%
Difference	+5	+21.0289	+2.5677%	+2685000	+83760000	+0.7954	+5.9342%	+21.8243	+4.4428%	+4.4428%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2758531	7004695576066024786136572769	28	92.500	1269642352408949688464 2⁴ × 16262303 × 4879545475543	2020-12-05	16262303	4879545475543	489,823,347	29,775	55,608

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-03-22T00:00:00	ANONYMOUS	v4_computers	15000	153750		-		-	-	0.003	-	-	0.706%
2002-01-02T00:00:00	ANONYMOUS	v4_computers	20000	240000		-		-	-	0.004	-	-	0.903%
2002-01-02T00:00:00	ANONYMOUS	v4_computers	50000	1500000		-		-	-	0.014	-	-	1.961%
2003-11-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.242%
2014-04-16T21:18:00	Jocelyn Larouche	Manual testing	60000	60000		-		-	-	0.007	-	-	0.609%
2014-04-22T10:35:00	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.011	-	-	0.838%
2014-10-19T12:31:00	Jocelyn Larouche	Manual testing	123268	123268		-		-	-	0.014	-	-	0.945%
2015-05-08T04:15:00	Squeeky_Squirrel	P4_2600	195000	6045000		-		-	-	0.058	-	-	3.539%
2017-01-03T20:36:24	mikr	MSI	2700000	84000000	12	-		-	-	0.798	-	-	7.679%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-04-11T00:00:00	netconx	v4_computers	2¹	2⁵⁹		-	-	0.028	-	-
2016-02-23T16:29:21	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.028	-	-
2009-01-31T09:24:00	Sturle Sunde	goose.ifi	2⁶⁰	2⁶¹		-	-	0.056	-	-
2012-03-21T21:17:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.111	-	-
2013-01-14T12:31:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.356	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.712	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.354	-	-
2016-02-05T15:45:59	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.709	-	-
2017-10-09T09:26:13	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.418	-	-
2019-02-21T01:08:07	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.84	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.548 GHz-days
Estimated T-Level:	3.150

Digits	B1	Curves	Complete	FacMiss
20	11000	63 / 100	0.630	53.091%
25	50000	63 / 280	0.225	79.819%

New Calculation Method

Total ECM effort:	6.548 GHz-days
Estimated T-Level:	3.150

Digits	B1	Complete	FacMiss
20	11000	2.423	8.865%
25	50000	0.224	79.916%
30	250000	0.014	98.596%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		57	5.924
50000	5000000	7004695576066024786136572769	6	0.624

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-14T17:06:00	willreid	jing	50000	5000000						3	0.312
2010-09-10T18:21:00	unconnected	xp-xxx	50000	5000000						3	0.312
2013-03-03T03:39:00	Donna Noble	opt4820	50000	5000000						3	0.312
2015-03-11T04:54:00	Bruce	desk16	50000	5000000						3	0.312
2016-02-13T21:11:42	Sintax	cloud2	50000	5000000						3	0.312
2016-05-15T13:30:01	lettp	Home	50000	5000000						3	0.312
2017-01-12T03:05:51	deo2016	deo2016.home.new	50000	5000000						3	0.312
2017-07-27T12:38:00	JMGarcia	jmgarcia-pW07	50000	5000000						3	0.312
2017-12-26T20:49:38	Sebastian Hornbostel	V2	50000	5000000						3	0.312
2018-10-01T04:58:43	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.312
2020-08-04T01:33:03	GAN	LMS-14	50000	5000000						3	0.312
2020-08-12T00:48:36	GAN	LMS-12	50000	5000000						3	0.312
2020-08-30T07:41:43	GAN	OSB-01	50000	5000000						7	0.728
2020-10-03T22:43:01	mnd9	75204b	50000	5000000						7	0.728
2020-10-29T20:48:22	GAN	AC-GR	50000	5000000						7	0.728
2020-12-05T12:40:12	rextherunt	ice	50000	5000000	7004695576066024786136572769	92.500	6	2		6	0.624

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-04-27T00:00:00	netconx	v4_computers	8A733B64E9E33033	0.213
1999-08-31T00:00:00	ANONYMOUS	v4_computers	6850E70167D7D5__	0.213
2000-03-27T00:00:00	ANONYMOUS	v4_computers	8A733B64E9E33033	0.213
2018-08-16T09:34:55	kkmrkkblmbrbk	old	8A733B64E9E33033	0.213

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 = 2700000, B2 = 84000000 (P-1 stage 2)

B1 = 2700000 (P-1 stage 1)

B1 = 195000, B2 = 6045000 (P-1 stage 2)

B1 = 195000 (P-1 stage 1)

B1 = 50000, B2 = 1500000 (P-1 stage 2)

B1 = 123268 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 240000 (P-1 stage 2)

B1 = 15000, B2 = 153750 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10²

10³

10⁴

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10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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