M2573057 Mersenne number exponent details

is 2 ^2573057 - 1

has 774568 decimal digits

takes 0.178 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	23.1650	67.6471%	3200000	112000000	0.9180	8.0800%	24.0830	70.2612%	2.6141%
PrimeNet	2⁵⁹	0.0298	62.7119%	11000	200000	0.0021	2.6897%	0.0320	63.7148%	1.0029%
GPU72	2⁶³	0.6203	65.0794%	12000	190000	0.0022	1.5045%	0.6225	65.6047%	0.5254%
Difference	+5	+22.5447	+2.5677%	+3188000	+111810000	+0.9158	+6.5755%	+23.4606	+4.6564%	+4.6564%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2573057	1321348997032702246762823	25	80.128	256766367210812323 331183 × 775300565581	2021-03-08	331183	775300565581	103,467	4,248.3	7,934.6

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-31T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.237%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	202500		-		-	-	0.003	-	-	0.762%
2010-12-21T11:03:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.265%
2011-01-10T23:58:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.532%
2011-04-18T08:11:00	James Heinrich	WHS	175000	4112500		-		-	-	0.039	-	-	3.174%
2016-06-22T08:05:30	mikr	MSI	3200000	112000000	12	-		-	-	0.918	-	-	8.080%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2016-02-23T16:29:16	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.030	-	-
2009-01-31T15:12:00	Sturle Sunde	giny.ifi	2⁶⁰	2⁶¹		-	-	0.060	-	-
2012-06-19T07:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.119	-	-
2013-01-23T08:30:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.382	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.763	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.452	-	-
2015-12-02T09:49:55	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.904	-	-
2017-08-20T12:59:32	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.808	-	-
2019-09-03T13:43:04	Yxinity	Manual testing	2⁶⁷	2⁶⁸		-	-	11.62	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	9.233 GHz-days
Estimated T-Level:	21.786

Digits	B1	Curves	Complete	FacMiss
20	11000	100 / 100	1.000	36.603%
25	50000	100 / 280	0.357	69.923%

New Calculation Method

Total ECM effort:	9.233 GHz-days
Estimated T-Level:	21.786

Digits	B1	Complete	FacMiss
20	11000	3.226	3.972%
25	50000	0.292	74.711%
30	250000	0.018	98.221%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		99	9.141
50000	5000000	1321348997032702246762823	1	0.092

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-17T16:30:00	Jürgen Decker	Q9550_home	50000	5000000						3	0.277
2010-05-13T01:59:00	Sebastian Hornbostel	W	50000	5000000						3	0.277
2012-10-19T19:33:00	Donna Noble	i3-2100t	50000	5000000						3	0.277
2014-04-27T10:23:00	Andy Incline	Office-PC	50000	5000000						3	0.277
2016-01-23T04:59:58	Jason U	Server7	50000	5000000						3	0.277
2016-03-13T20:45:22	Jason U	Server7	50000	5000000						3	0.277
2016-08-03T18:37:29	lettp	Home	50000	5000000						3	0.277
2017-05-27T06:29:52	Bruce	eleven	50000	5000000						3	0.277
2017-10-09T01:50:01	Lelikoid	QH	50000	5000000						3	0.277
2018-04-06T08:44:19	Bruce	eleven	50000	5000000						3	0.277
2019-01-07T04:08:08	-Anonymous-	Videoserver	50000	5000000						3	0.277
2020-06-24T14:18:13	LaurV	3tits	50000	5000000						3	0.277
2020-07-02T23:30:45	Ahmed Azhad	colab	50000	5000000						3	0.277
2020-07-09T18:47:18	mnd9	office2	50000	5000000						3	0.277
2020-07-15T09:14:55	GAN	LMS-17	50000	5000000						3	0.277
2020-07-22T10:49:12	GAN	KL-10	50000	5000000						3	0.277
2020-07-28T02:45:23	GAN	LMS-01	50000	5000000						3	0.277
2020-08-04T12:04:23	J.R. Allen	lapasus	50000	5000000						3	0.277
2020-08-13T10:52:46	GAN	KL-SCH04	50000	5000000						3	0.277
2020-09-01T20:30:27	mnd9	libproj	50000	5000000						7	0.646
2020-10-05T07:55:56	mnd9	75204b	50000	5000000						7	0.646
2020-10-30T16:03:49	mnd9	75204	50000	5000000						7	0.646
2020-12-05T18:04:12	RIHATEC	i7-3770K	50000	5000000						7	0.646
2021-01-07T05:36:21	Gerry Snyder	Gerry-Workstation	50000	5000000						7	0.646
2021-02-06T17:58:42	Zenzoma	AMD3970X	50000	5000000						7	0.646
2021-03-08T20:03:51	mnd9	50869	50000	5000000	1321348997032702246762823	80.128	1	2	1742510907557758	1	0.092

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-04-13T00:00:00	ANONYMOUS	v4_computers	EFAAD39C4D519343	0.178
2018-06-17T06:23:57	kkmrkkblmbrbk	old	EFAAD39C4D519343	0.178

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-03-09T11:26:01

_p95holder_

TFL16_PRPt11-E_b

1321348997032702246762823

1861A55FA276E1F2

2021-03-09T16:39:00

mrh

lanai

1321348997032702246762823

1861A55FA276E1F2

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 = 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

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-03-09T16:39:00+00:00

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