M2989409 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	19.9387	67.6471%	3000000	90000000	0.9552	7.8877%	20.8939	70.1990%	2.5519%
PrimeNet	2⁶⁰	0.0514	63.3333%	12000	220000	0.0029	2.5135%	0.0543	64.2549%	0.9216%
GPU72	2⁶⁴	1.1906	65.6250%	13000	200000	0.0029	1.3860%	1.1935	66.1014%	0.4764%
Difference	+4	+18.7480	+2.0221%	+2987000	+89800000	+0.9523	+6.5018%	+19.7004	+4.0976%	+4.0976%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2989409	541120752083251030623871	24	78.840	90506309455021215 3 × 5 × 7 × 861964851952583	2021-02-25	7	861964851952583	33,044	5,795,660	10,824,679

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-13T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.247%
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.146%
2010-10-22T20:31:00	markr	tiny	100000	2025000		-		-	-	0.025	-	-	2.495%
2016-06-22T02:55:59	Jocelyn Larouche	Manual testing	198400	4050000	6	-		-	-	0.050	-	-	3.296%
2017-07-10T01:11:32	Jocelyn Larouche	low 4M	396800	3968000	6	-		-	-	0.073	-	-	3.598%
2019-11-09T08:22:59	BigBrother	Winston	3000000	90000000	12	-		-	-	0.955	-	-	7.888%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.051	-	-
1999-09-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.051	-	-
2009-02-13T21:31:00	Sturle Sunde	othello.ifi	2⁶⁰	2⁶¹		-	-	0.051	-	-
2011-11-29T06:00:00	Grant McCracken	home	2⁶¹	2⁶²		-	-	0.103	-	-
2013-01-07T13:51:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.328	-	-
2015-02-06T00:11:00	lycorn	Manual testing	2⁶³	2⁶⁴		-	-	0.657	-	-
2015-02-06T00:12:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	1.250	-	-
2016-02-29T09:29:40	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.500	-	-
2017-12-07T01:23:26	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.999	-	-
2018-12-28T09:55:51	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.00	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.500 GHz-days
Estimated T-Level:	2.800

Digits	B1	Curves	Complete	FacMiss
20	11000	56 / 100	0.560	56.960%
25	50000	56 / 280	0.200	81.844%

New Calculation Method

Total ECM effort:	6.500 GHz-days
Estimated T-Level:	2.800

Digits	B1	Complete	FacMiss
20	11000	1.806	16.424%
25	50000	0.163	84.937%
30	250000	0.010	99.000%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		52	6.035
50000	5000000	541120752083251030623871	4	0.464

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-05T20:06:00	Martti Järvi	Wanda	50000	5000000						3	0.348
2011-05-11T13:54:00	sannerud.com	Jens2010	50000	5000000						3	0.348
2013-09-03T10:01:00	Youcef L	breitner	50000	5000000						3	0.348
2016-01-13T03:40:51	Bruce	Desk7	50000	5000000						3	0.348
2017-07-13T02:41:04	Lelikoid	QH	50000	5000000						3	0.348
2020-09-14T18:11:58	MarkS	desktop-i7	50000	5000000						7	0.812
2020-10-17T10:03:53	mnd9	libproj	50000	5000000						7	0.812
2020-11-18T09:27:12	LaurV	debilis	50000	5000000						7	0.812
2020-12-22T20:34:07	IanGlencross	glenx24	50000	5000000						7	0.812
2021-01-07T02:47:53	Cork	Manual testing	50000	5000000						7	0.812
2021-01-23T19:34:10	Peredron	Peredron	50000	5000000						1	0.116
2021-01-27T08:39:01	Peredron	Peredron	50000	5000000						1	0.116
2021-02-25T16:29:18	daveward2005	Davy	50000	5000000	541120752083251030623871	78.840	4	2	5942340179852823	4	0.464

date	userid	compid	res64	spent (GHz-days)
1999-05-30T00:00:00	ANONYMOUS	v4_computers	CE680D6ECB24E7B9	0.254
1999-09-07T00:00:00	ANONYMOUS	v4_computers	CE680D6ECB24E7B9	0.254
2018-10-22T03:22:53	kkmrkkblmbrbk	old	CE680D6ECB24E7B9	0.254

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 = 3000000, B2 = 90000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 396800, B2 = 3968000 (P-1 stage 2)

B1 = 198400, B2 = 4050000 (P-1 stage 2)

B1 = 396800 (P-1 stage 1)

B1 = 100000, B2 = 2025000 (P-1 stage 2)

B1 = 198400 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

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

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

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