M2567821 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	23.2122	67.6471%	3200000	112000000	0.9180	8.0784%	24.1302	70.2606%	2.6136%
PrimeNet	2⁵⁹	0.0299	62.7119%	11000	200000	0.0021	2.6887%	0.0320	63.7144%	1.0026%
GPU72	2⁶³	0.6215	65.0794%	12000	180000	0.0021	1.4801%	0.6237	65.5962%	0.5169%
Difference	+5	+22.5907	+2.5677%	+3188000	+111820000	+0.9159	+6.5983%	+23.5066	+4.6644%	+4.6644%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2567821	620485742181444150047621953	27	89.004	120819508482375553056 2⁵ × 3 × 23 × 4679 × 11694588649483	2020-12-23	4679	11694588649483	91,688,016	64,081	119,685

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-23T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.237%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	202500		-		-	-	0.003	-	-	0.761%
2010-12-21T01:09:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.265%
2011-01-03T22:20:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.367%
2011-01-10T23:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.532%
2011-04-15T21:20:00	James Heinrich	WHS	175000	4112500		-		-	-	0.039	-	-	3.173%
2016-05-29T07:42:25	mikr	MSI	3200000	112000000	12	-		-	-	0.918	-	-	8.078%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15T00:00:00	Stephan Grupp	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2016-02-23T16:29:16	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.030	-	-
2009-01-27T23:50:00	Sturle Sunde	dittersdorf.ifi	2⁶⁰	2⁶¹		-	-	0.060	-	-
2012-06-17T16:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.120	-	-
2013-01-23T08:30:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.382	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.765	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.455	-	-
2015-11-08T21:03:02	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.910	-	-
2017-08-13T10:39:20	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.820	-	-
2019-05-13T13:38:12	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.64	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.220 GHz-days
Estimated T-Level:	4.250

Digits	B1	Curves	Complete	FacMiss
20	11000	85 / 100	0.850	42.559%
25	50000	85 / 280	0.304	73.778%

New Calculation Method

Total ECM effort:	8.220 GHz-days
Estimated T-Level:	4.250

Digits	B1	Complete	FacMiss
20	11000	2.776	6.226%
25	50000	0.250	77.888%
30	250000	0.015	98.476%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	50000		7	0.375
50000	5000000		81	7.477
50000	5000000	620485742181444150047621953	4	0.369

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-20T10:27:00	Lukasz Wrobel	LINUX_01	50000	5000000						3	0.277
2010-05-13T20:38:00	SubPrime	abd0	50000	5000000						3	0.277
2012-10-19T16:20:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.277
2014-05-01T17:22:00	Syntony	Hadfield	50000	5000000						3	0.277
2015-08-14T14:22:00	guru	w6	50000	5000000						3	0.277
2016-03-12T17:48:37	Jason U	Server7	50000	5000000						3	0.277
2016-08-02T15:20:32	lettp	Home	50000	5000000						3	0.277
2017-05-25T13:08:07	Bruce	eleven	50000	5000000						3	0.277
2017-10-04T13:33:43	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.277
2018-04-04T14:45:25	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.277
2019-01-04T18:20:10	Dylan Delgado	laptop-i55200	50000	5000000						30	2.769
2020-09-14T02:09:06	-Anonymous-		50000	50000						7	0.375
2020-09-16T10:59:23	daveward2005	MW	50000	5000000						7	0.646
2020-10-16T04:53:51	GAN	KA-AC	50000	5000000						7	0.646
2020-11-15T18:55:01	mnd9	27016b	50000	5000000						7	0.646
2020-12-23T12:12:49	daveward2005	Dave2	50000	5000000	620485742181444150047621953	89.004	4	2	2072334333143346	4	0.369

date	userid	compid	res64	spent (GHz-days)
1999-04-13T00:00:00	Stephan Grupp	v4_computers	14F921551EC20868	0.178
2018-06-16T02:13:39	kkmrkkblmbrbk	old	14F921551EC20868	0.178

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 = 3200000, B2 = 112000000 (P-1 stage 2)

B1 = 3200000 (P-1 stage 1)

B1 = 175000, B2 = 4112500 (P-1 stage 2)

B1 = 175000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 202500 (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

10²

10³

10⁴

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10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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