M2298613 Mersenne number exponent details

Residue

Status

L-L

FD40205CD20507D5

double-checked

PRP

E6CE3F63B38B97__

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁹	51.9386	68.1159%	500000	10000000	0.0997	3.9564%	52.0383	69.3774%	1.2614%
PrimeNet	2⁵⁸	0.0167	62.0690%	10000	190000	0.0019	2.9277%	0.0186	63.1795%	1.1105%
GPU72	2⁶²	0.2673	64.5161%	12000	200000	0.0022	1.7373%	0.2695	65.1326%	0.6165%
Difference	+7	+51.6713	+3.5998%	+488000	+9800000	+0.0975	+2.2190%	+51.7688	+4.2448%	+4.2448%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

51.9386

68.1159%

500000

10000000

0.0997

3.9564%

52.0383

69.3774%

1.2614%

PrimeNet

2⁵⁸

0.0167

62.0690%

10000

190000

0.0019

2.9277%

0.0186

63.1795%

1.1105%

GPU72

2⁶²

0.2673

64.5161%

12000

200000

0.0022

1.7373%

0.2695

65.1326%

0.6165%

Difference

+51.6713

+3.5998%

+488000

+9800000

+0.0975

+2.2190%

+51.7688

+4.2448%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2298613	157901836750271690509571687	27	87.029	34347199104475544711 47 × 97 × 7533932683587529	2021-09-20	97	7533932683587529	17,386,852	40,207,762	75,096,902

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2298613

157901836750271690509571687

87.029

34347199104475544711
47 × 97 × 7533932683587529

2021-09-20

7533932683587529

17,386,852

40,207,762

75,096,902

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2003-08-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.185%
2010-10-20T18:30:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.585%
2011-01-17T14:53:00	Oscar Östlin		90000	1755000		-		-	-	0.018	-	-	2.006%
2013-11-16T02:26:00	c10ck3r	Manual testing	500000	10000000		-		-	-	0.100	-	-	3.956%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2003-08-08T00:00:00

ANONYMOUS

v4_computers

2048

204800

0.001

-

-

0.185%

2010-10-20T18:30:00

Oscar Östlin

75011

0.007

-

-

0.585%

2011-01-17T14:53:00

Oscar Östlin

90000

1755000

0.018

-

-

2.006%

2013-11-16T02:26:00

c10ck3r

Manual testing

500000

10000000

0.100

-

-

3.956%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:11	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.067	-	-
2009-01-15T22:48:00	Sturle Sunde	gonsha.ifi	2⁶⁰	2⁶¹		-	-	0.067	-	-
2012-05-12T08:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.134	-	-
2013-01-23T08:24:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.427	-	-
2015-03-12T10:50:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.854	-	-
2015-03-12T10:50:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.625	-	-
2015-11-04T09:56:28	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.251	-	-
2017-05-27T13:18:47	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.502	-	-
2019-03-18T11:45:41	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.00	-	-
2021-06-10T09:22:49	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	26.01	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.892 GHz-days
Estimated T-Level:	22.982

Digits	B1	Curves	Complete	FacMiss
20	11000	167 / 100	1.670	18.667%
25	50000	167 / 280	0.596	55.019%

New Calculation Method

Total ECM effort:	14.892 GHz-days
Estimated T-Level:	22.982

Digits	B1	Complete	FacMiss
20	11000	5.415	0.445%
25	50000	0.489	61.303%
30	250000	0.030	97.029%
35	1000000	0.001	99.862%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		146	12.92
50000	5000000	157901836750271690509571687	6	0.531
50000	5150000		7	0.627
50000	6750000		7	0.709
60000	6000000		1	0.106

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-27T15:41:00	bladerunner	Nebuchadnezzar	50000	5000000						3	0.265
2010-01-07T13:41:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.265
2011-11-19T17:28:00	S36049	Wolle5	50000	5000000						3	0.265
2013-09-21T02:14:00	arnaud	srv-630	50000	5000000						3	0.265
2015-04-12T11:52:00	Jason U	Server7	50000	5000000						3	0.265
2016-02-14T06:17:46	Jason U	Server7	50000	5000000						3	0.265
2016-04-17T19:11:23	Bruce	Desk6	50000	5000000						3	0.265
2016-08-04T20:52:54	Bruce	Desk6	50000	5000000						3	0.265
2017-01-05T03:18:29	Bruce	Desk6	50000	5000000						3	0.265
2017-08-15T17:52:52	Bruce	Desk6	50000	5000000						3	0.265
2018-01-17T12:32:02	Bruce	Desk6	50000	5000000						3	0.265
2018-07-15T01:20:29	Bruce	Desk6	50000	5000000						3	0.265
2019-10-09T13:34:22	monsted	rootweiler	50000	5000000						3	0.265
2020-03-06T09:11:55	mnd9	75211backdoorb	50000	5000000						3	0.265
2020-03-13T09:34:55	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.265
2020-03-21T05:42:58	MarkS	desktop-i7	50000	5000000						3	0.265
2020-04-02T20:55:05	mnd9	colab	50000	5000000						3	0.265
2020-04-16T03:57:21	nranks	wlaptop	50000	5000000						3	0.265
2020-04-27T22:47:35	mnd9	libproj	50000	5000000						3	0.265
2020-05-03T17:09:38	Oliver Kruse	IOS-1	50000	5000000						3	0.265
2020-05-15T09:11:28	mnd9	libproj	50000	5000000						3	0.265
2020-06-02T13:44:15	nordi	sweet16	50000	5000000						3	0.265
2020-06-21T10:09:02	mnd9	touchdown	50000	5000000						3	0.265
2020-06-30T21:02:14	GAN	LMS-18	50000	5000000						3	0.265
2020-07-07T16:45:11	GAN	LMS-02	50000	5000000						3	0.265
2020-07-13T22:46:10	GAN	LMS-06	50000	5000000						3	0.265
2020-07-20T12:41:47	mnd9	libproj	50000	5000000						3	0.265
2020-07-26T08:07:15	GAN	LMS-14	50000	5000000						3	0.265
2020-08-02T18:15:24	daveward2005	Dave2	50000	5000000						3	0.265
2020-08-10T13:19:55	daveward2005	Dave2	50000	5000000						3	0.265
2020-08-25T07:39:26	GAN	OSK-SCH03	50000	5000000						7	0.619
2020-09-30T02:46:51	LaurV	3tits	50000	5000000						7	0.619
2020-10-23T23:11:28	Albrecht Heeffer	R7-3800X	50000	5000000						7	0.619
2020-11-28T06:25:14	Peredron	Peredron2	60000	6000000						1	0.106
2020-12-09T19:49:26	RIHATEC	i7-3770K	50000	5000000						7	0.619
2021-01-11T06:16:54	C.D.B.	i7-6850K	50000	5000000						7	0.619
2021-02-11T04:57:38	mnd9	50869	50000	5000000						7	0.619
2021-03-11T08:57:03	Gerry Snyder	Gerry-Workstation	50000	5000000						7	0.619
2021-04-20T09:42:07	IanGlencross	glenx24	50000	5000000						7	0.619
2021-06-09T11:01:53	kutens	arcturus	50000	5150000						7	0.627
2021-07-20T16:57:12	kutens	vega	50000	6750000						7	0.709
2021-09-20T21:01:29	daveward2005	Dave2	50000	5000000	157901836750271690509571687	87.029	6	2	333461729054209	6	0.531

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	FD40205CD20507D5	0.155
2018-04-30T06:58:33	kkmrkkblmbrbk	old	FD40205CD20507D5	0.155

date

userid

compid

res64

spent (GHz-days)

1999-03-15T00:00:00

ANONYMOUS

v4_computers

FD40205CD20507D5

0.155

2018-04-30T06:58:33

kkmrkkblmbrbk

old

FD40205CD20507D5

0.155

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