M2259217 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	26.3830	67.6471%	1000000	20000000	0.1940	5.3775%	26.5770	69.3868%	1.7398%
PrimeNet	2⁵⁸	0.0170	62.0690%	10000	190000	0.0019	2.9184%	0.0189	63.1759%	1.1070%
GPU72	2⁶²	0.2719	64.5161%	12000	190000	0.0021	1.7061%	0.2740	65.1215%	0.6054%
Difference	+6	+26.1110	+3.1309%	+988000	+19810000	+0.1920	+3.6713%	+26.3030	+4.2653%	+4.2653%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2259217	348395472999707409530239	24	78.205	77105358405081807 3 × 131 × 196196840725399	2021-05-08	131	196196840725399	39,923	1,019,095	1,903,386

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2010-11-06T16:27:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.200%
2010-11-12T11:44:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.357%
2011-01-05T06:35:00	markr	tiny	100000	2075000		-		-	-	0.020	-	-	2.405%
2014-09-02T00:10:00	Jocelyn Larouche	Manual testing	128410	128410		-		-	-	0.012	-	-	0.933%
2016-03-26T08:01:33	Jocelyn Larouche	Manual testing	342144	3421440	6	-		-	-	0.049	-	-	3.291%
2019-06-29T12:08:11	BigBrother	Winston	1000000	20000000	12	-		-	-	0.194	-	-	5.377%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:10	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.068	-	-
2009-01-12T04:07:00	Sturle Sunde	gluck.ifi	2⁶⁰	2⁶¹		-	-	0.068	-	-
2012-05-05T07:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.136	-	-
2013-01-23T08:24:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.435	-	-
2015-03-10T10:44:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.869	-	-
2015-03-10T10:44:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.654	-	-
2015-10-29T11:36:23	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.308	-	-
2017-01-16T00:47:35	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.615	-	-
2019-05-13T13:38:16	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.23	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	11.083 GHz-days
Estimated T-Level:	22.304

Digits	B1	Curves	Complete	FacMiss
20	11000	129 / 100	1.290	27.349%
25	50000	129 / 280	0.461	63.031%

New Calculation Method

Total ECM effort:	11.083 GHz-days
Estimated T-Level:	22.304

Digits	B1	Complete	FacMiss
20	11000	4.962	0.700%
25	50000	0.459	63.187%
30	250000	0.029	97.146%
35	1000000	0.001	99.865%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		124	10.65
50000	5000000	348395472999707409530239	5	0.430

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-30T16:02:00	ksims	ZhViZCJBe1505	50000	5000000						3	0.258
2010-05-26T14:47:00	James Hintz	nana	50000	5000000						3	0.258
2011-10-26T17:59:00	S36049	Wolle5	50000	5000000						3	0.258
2013-08-19T02:29:00	arnaud	srv-630	50000	5000000						3	0.258
2015-04-02T06:41:00	Jason U	Server7	50000	5000000						3	0.258
2016-02-04T13:24:55	Jason U	Server7	50000	5000000						3	0.258
2016-03-31T22:07:24	Bruce	Desk6	50000	5000000						3	0.258
2016-07-21T05:58:31	Bruce	Desk6	50000	5000000						3	0.258
2016-12-07T15:11:51	Bruce	Desk6	50000	5000000						3	0.258
2017-07-05T11:35:05	Bruce	Desk6	50000	5000000						3	0.258
2017-12-19T10:28:56	Bruce	Desk6	50000	5000000						3	0.258
2018-05-29T16:48:51	Bruce	Desk6	50000	5000000						3	0.258
2019-06-01T16:10:26	Stefan G. Hoffmann	PC-HRW-2017-Dell	50000	5000000						3	0.258
2020-02-24T08:46:06	mnd9	kitchen	50000	5000000						3	0.258
2020-03-02T08:38:26	kracker	O0	50000	5000000						3	0.258
2020-03-08T04:08:39	mnd9	office2	50000	5000000						3	0.258
2020-03-15T18:04:01	daveward2005	MW	50000	5000000						3	0.258
2020-03-24T20:12:53	kracker	O0	50000	5000000						3	0.258
2020-04-06T06:53:13	Brett Walker	brain	50000	5000000						3	0.258
2020-04-20T03:07:23	nranks	wlaptop	50000	5000000						3	0.258
2020-04-27T23:24:30	Oliver Kruse	IOS-1	50000	5000000						3	0.258
2020-05-07T13:38:43	mnd9	libproj	50000	5000000						3	0.258
2020-05-22T10:42:04	mat10243x	K3	50000	5000000						3	0.258
2020-06-08T08:52:56	mnd9	50871b	50000	5000000						3	0.258
2020-06-24T12:21:54	MarkS	laptop64	50000	5000000						3	0.258
2020-07-03T03:03:22	GAN	LMS-11	50000	5000000						3	0.258
2020-07-09T19:34:01	GAN	OSK-02	50000	5000000						3	0.258
2020-07-15T13:33:07	GAN	LMS-15	50000	5000000						3	0.258
2020-07-21T20:31:58	Ahmed Azhad	c5.4xlarge.azf	50000	5000000						3	0.258
2020-07-28T08:07:23	IanGlencross	glenx24	50000	5000000						3	0.258
2020-08-04T19:21:15	IanGlencross	glenx24	50000	5000000						3	0.258
2020-08-12T22:32:47	Yuji HASEGAWA	lat5280	50000	5000000						3	0.258
2020-09-01T07:57:26	mnd9	f4	50000	5000000						7	0.601
2020-10-05T08:45:03	MarkS	desktop-i7	50000	5000000						7	0.601
2020-10-31T13:44:32	Albrecht Heeffer	R7-3800X	50000	5000000						7	0.601
2020-12-06T09:22:13	RIHATEC	i7-3770K	50000	5000000						7	0.601
2021-05-08T00:52:54	Zenzoma	AM3700X_1	50000	5000000	348395472999707409530239	78.205	5	2	3434107338427649	5	0.430

date	userid	compid	res64	spent (GHz-days)
1999-03-01T00:00:00	ANONYMOUS	v4_computers	29F53F045D82E9__	0.149

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 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 342144, B2 = 3421440 (P-1 stage 2)

B1 = 342144 (P-1 stage 1)

B1 = 100000, B2 = 2075000 (P-1 stage 2)

B1 = 128410 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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