M2250461 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	2⁶⁹	53.0499	68.1159%	1000000	20000000	0.1940	4.8998%	53.2440	69.6782%	1.5623%
PrimeNet	2⁵⁸	0.0171	62.0690%	10000	190000	0.0019	2.9163%	0.0190	63.1752%	1.1062%
GPU72	2⁶²	0.2730	64.5161%	11000	190000	0.0020	1.6600%	0.2750	65.1052%	0.5890%
Difference	+7	+52.7769	+3.5998%	+989000	+19810000	+0.1920	+3.2398%	+52.9690	+4.5730%	+4.5730%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2250461	91296294649961187458295551	26	86.239	20283909530083211275 5² × 19 × 42702967431754129	2021-09-04	25	42702967431754129	9,217,067	221,809,889	414,279,102

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-04-03T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.183%
2010-11-06T12:26:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.166%
2010-11-11T22:09:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.302%
2011-01-06T10:04:00	markr	tiny	100000	2075000		-		-	-	0.020	-	-	2.131%
2014-09-02T00:10:00	Jocelyn Larouche	Manual testing	128521	128521		-		-	-	0.012	-	-	0.812%
2016-03-02T12:01:16	Jocelyn Larouche	Manual testing	342144	6158592	12	-		-	-	0.063	-	-	3.386%
2019-06-27T17:39:50	BigBrother	Winston	1000000	20000000	12	-		-	-	0.194	-	-	4.900%

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	-	-
2009-01-11T11:37:00	Sturle Sunde	wright.ifi	2⁶⁰	2⁶¹		-	-	0.068	-	-
2012-05-04T10:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.136	-	-
2013-12-04T06:19:00	LaurV	Manual testing	2⁶²	2⁶³		-	-	0.436	-	-
2015-03-10T10:44:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.872	-	-
2015-03-10T10:44:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.660	-	-
2015-10-27T09:37:31	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.321	-	-
2017-01-05T21:20:49	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.641	-	-
2019-05-20T13:24:28	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.28	-	-
2021-06-24T13:44:36	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	26.56	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.605 GHz-days
Estimated T-Level:	23.036

Digits	B1	Curves	Complete	FacMiss
20	11000	170 / 100	1.700	18.113%
25	50000	170 / 280	0.607	54.431%

New Calculation Method

Total ECM effort:	14.605 GHz-days
Estimated T-Level:	23.036

Digits	B1	Complete	FacMiss
20	11000	5.491	0.412%
25	50000	0.496	60.912%
30	250000	0.031	96.993%
35	1000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		159	13.65
50000	5000000	91296294649961187458295551	4	0.343
50000	5150000		7	0.609

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-28T12:30:00	dachshund	Ann	50000	5000000						3	0.258
2010-05-06T20:54:00	James Hintz	nana	50000	5000000						3	0.258
2011-10-21T23:11:00	Dmitry B. Khachaturov	dix-home	50000	5000000						3	0.258
2013-07-23T12:25:00	Lukasz Wrobel	i-1	50000	5000000						3	0.258
2015-06-17T18:57:00	guru	w6	50000	5000000						3	0.258
2015-07-11T07:55:00	S36049	Wolle5	50000	5000000						3	0.258
2016-03-29T15:07:41	lettp	Home	50000	5000000						3	0.258
2016-07-18T02:05:30	Bruce	Desk6	50000	5000000						3	0.258
2016-12-04T06:13:34	Bruce	Desk6	50000	5000000						3	0.258
2017-06-29T04:52:14	Bruce	Desk6	50000	5000000						3	0.258
2017-12-12T19:58:23	Bruce	Desk6	50000	5000000						3	0.258
2018-05-18T17:59:15	Bruce	Desk6	50000	5000000						3	0.258
2019-04-28T00:14:03	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.258
2020-02-21T01:25:43	Nesowa	6700T	50000	5000000						3	0.258
2020-02-27T23:03:01	mnd9	25836b	50000	5000000						3	0.258
2020-03-05T17:29:04	Sergey Nosov	TS140-02	50000	5000000						3	0.258
2020-03-13T03:49:24	Nesowa	entropy_generator_2	50000	5000000						3	0.258
2020-03-27T02:32:03	cappy95833	HomePC	50000	5000000						3	0.258
2020-04-01T16:46:04	Bommer	3900X	50000	5000000						3	0.258
2020-04-13T21:49:37	EricP	Cannonfodder	50000	5000000						3	0.258
2020-04-24T16:40:24	nordi	sweet16	50000	5000000						3	0.258
2020-05-02T09:02:10	daveward2005	MW	50000	5000000						3	0.258
2020-05-16T10:23:27	nokno	leo221	50000	5000000						3	0.258
2020-05-30T09:29:51	mnd9	touchdown	50000	5000000						3	0.258
2020-06-21T01:05:03	LaurV	3tits	50000	5000000						3	0.258
2020-06-30T00:44:48	GAN	LMS-16	50000	5000000						3	0.258
2020-07-07T12:49:16	mnd9	25836b	50000	5000000						3	0.258
2020-07-13T09:55:10	GAN	OSB-02	50000	5000000						3	0.258
2020-07-19T08:02:48	GAN	LMS-07	50000	5000000						3	0.258
2020-07-25T14:35:29	GAN	LMS-12	50000	5000000						3	0.258
2020-08-01T20:12:01	GAN	OSB-02	50000	5000000						3	0.258
2020-08-09T20:15:30	GAN	XPS	50000	5000000						3	0.258
2020-08-23T21:50:48	Nesowa	6700T	50000	5000000						7	0.601
2020-09-24T13:36:46	IanGlencross	glenx24	50000	5000000						7	0.601
2020-10-22T14:16:36	mnd9	50869	50000	5000000						7	0.601
2020-11-25T08:27:25	IanGlencross	glenx24	50000	5000000						7	0.601
2020-12-30T20:17:43	mnd9	75211backdoor	50000	5000000						7	0.601
2021-01-30T19:53:47	arachnotron	DellLaptop	50000	5000000						7	0.601
2021-02-28T20:27:13	mnd9	l2lounge	50000	5000000						7	0.601
2021-04-05T07:14:32	daveward2005	Dave2	50000	5000000						7	0.601
2021-05-24T03:01:31	kutens	canopus	50000	5150000						7	0.609
2021-08-22T13:09:50	tottenhoff	Garage-Band-003	50000	5000000						7	0.601
2021-09-04T21:13:00	mnd9	27016b	50000	5000000	91296294649961187458295551	86.239	4	2	4255107824809696	4	0.343

date	userid	compid	res64	spent (GHz-days)
1999-03-01T00:00:00	ANONYMOUS	v4_computers	716983849F666392	0.148
2018-04-23T01:14:59	kkmrkkblmbrbk	old	716983849F666392	0.148

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 = 6158592 (P-1 stage 2)

B1 = 342144 (P-1 stage 1)

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

B1 = 128521 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10⁰

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10¹⁷

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