M2289961 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	26.0288	67.6471%	743920	7439200	0.1086	4.2802%	26.1374	69.0318%	1.3848%
PrimeNet	2⁵⁸	0.0168	62.0690%	10000	190000	0.0019	2.9256%	0.0187	63.1787%	1.1097%
GPU72	2⁶²	0.2683	64.5161%	12000	200000	0.0022	1.7360%	0.2705	65.1321%	0.6160%
Difference	+6	+25.7605	+3.1309%	+731920	+7239200	+0.1064	+2.5442%	+25.8669	+3.8997%	+3.8997%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2289961	1073281306404150081487	22	69.863	234344887621263 3³ × 8679440282269	2020-07-17	27	8679440282269	84.717	46,321	86,515

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-09T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.229%
2003-02-24T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.003	-	-	0.469%
2016-10-07T05:48:05	Jocelyn Larouche	low 4M	144179	15728640	12	-		-	-	0.097	-	-	3.923%
2017-02-25T21:08:08	Jocelyn Larouche	low 4M	298966	2989660	6	-		-	-	0.044	-	-	3.139%
2017-03-24T21:07:32	Jocelyn Larouche	low 4M	358759	3587590	6	-		-	-	0.052	-	-	3.353%
2017-03-28T11:59:29	Jocelyn Larouche	low 4M	430510	4305100	6	-		-	-	0.063	-	-	3.575%
2017-04-01T09:06:04	Jocelyn Larouche	low 4M	516612	5166120	6	-		-	-	0.075	-	-	3.803%
2017-04-04T20:17:32	Jocelyn Larouche	low 4M	619934	6199340	12	-		-	-	0.091	-	-	4.038%
2017-04-07T19:41:21	Jocelyn Larouche	low 4M	743920	7439200	12	-		-	-	0.109	-	-	4.280%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-03-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.034	-	-
2016-02-23T16:29:11	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.034	-	-
2009-01-11T14:48:00	Sturle Sunde	hindemith.ifi	2⁶⁰	2⁶¹		-	-	0.067	-	-
2012-05-11T22:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.134	-	-
2013-12-06T02:46:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.429	-	-
2015-03-12T10:50:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.857	-	-
2015-03-12T10:50:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.632	-	-
2015-11-02T09:33:40	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.263	-	-
2017-05-21T02:33:15	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.527	-	-
2019-06-17T12:14:56	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.05	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.075 GHz-days
Estimated T-Level:	4.000

Digits	B1	Curves	Complete	FacMiss
20	11000	80 / 100	0.800	44.752%
25	50000	80 / 280	0.286	75.109%

New Calculation Method

Total ECM effort:	7.075 GHz-days
Estimated T-Level:	4.000

Digits	B1	Complete	FacMiss
20	11000	2.581	7.573%
25	50000	0.233	79.197%
30	250000	0.014	98.574%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		78	6.898
50000	5000000	1073281306404150081487	2	0.177

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-14T13:05:00	paulie	iMac3.4	50000	5000000						3	0.265
2010-07-06T21:39:00	James Hintz	nana	50000	5000000						3	0.265
2011-11-16T01:42:00	S36049	Wolle5	50000	5000000						3	0.265
2013-09-13T11:28:00	arnaud	srv-630	50000	5000000						3	0.265
2015-04-09T13:24:00	Bruce	desk16	50000	5000000						3	0.265
2016-02-12T16:36:04	Jason U	Server7	50000	5000000						3	0.265
2016-04-14T01:29:04	Bruce	Desk6	50000	5000000						3	0.265
2016-08-01T06:59:17	Bruce	Desk6	50000	5000000						3	0.265
2016-12-28T21:15:25	Bruce	Desk6	50000	5000000						3	0.265
2017-08-04T06:07:46	Bruce	Desk6	50000	5000000						3	0.265
2018-01-08T11:20:03	Bruce	Desk6	50000	5000000						3	0.265
2018-07-07T04:52:36	Bruce	Desk6	50000	5000000						3	0.265
2019-09-13T09:55:40	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.265
2020-03-04T07:24:35	mnd9	75211backdoorb	50000	5000000						3	0.265
2020-03-11T06:56:21	Nesowa	entropy_generator_2	50000	5000000						3	0.265
2020-03-18T04:46:23	MarkS	desktop-i7	50000	5000000						3	0.265
2020-03-28T21:24:40	MarkS	laptop64	50000	5000000						3	0.265
2020-04-10T07:33:29	mnd9	libproj	50000	5000000						3	0.265
2020-04-22T14:29:21	Keysarecool	Boat_Anchor	50000	5000000						3	0.265
2020-04-30T16:46:43	mnd9	50871b	50000	5000000						3	0.265
2020-05-11T09:11:11	Brett Walker	brain	50000	5000000						3	0.265
2020-05-26T22:12:25	mnd9	libproj	50000	5000000						3	0.265
2020-06-13T17:52:58	daveward2005	Davy	50000	5000000						3	0.265
2020-06-29T04:43:18	mnd9	75203b	50000	5000000						3	0.265
2020-07-05T07:47:49	GAN	OSB-01	50000	5000000						3	0.265
2020-07-12T02:00:55	GAN	XPS	50000	5000000						3	0.265
2020-07-17T14:54:55	GAN	LMS-01	50000	5000000	1073281306404150081487	69.863	2	2	5189945048902292	2	0.177

date	userid	compid	res64	spent (GHz-days)
1999-03-01T00:00:00	ANONYMOUS	v4_computers	C27D4DC81E26F7EA	0.155
1999-04-13T00:00:00	ANONYMOUS	v4_computers	C27D4DC81E26F7EA	0.155

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 = 743920, B2 = 7439200 (P-1 stage 2)

B1 = 144179, B2 = 15728640 (P-1 stage 2)

B1 = 619934, B2 = 6199340 (P-1 stage 2)

B1 = 516612, B2 = 5166120 (P-1 stage 2)

B1 = 743920 (P-1 stage 1)

B1 = 430510, B2 = 4305100 (P-1 stage 2)

B1 = 619934 (P-1 stage 1)

B1 = 358759, B2 = 3587590 (P-1 stage 2)

B1 = 516612 (P-1 stage 1)

B1 = 298966, B2 = 2989660 (P-1 stage 2)

B1 = 430510 (P-1 stage 1)

B1 = 358759 (P-1 stage 1)

B1 = 298966 (P-1 stage 1)

B1 = 144179 (P-1 stage 1)

B1 = 4096, B2 = 409600 (P-1 stage 2)

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

B1 = 4096 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

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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