M2306627 Mersenne number exponent details

Residue

Status

L-L

988FDE0B0E731C8E

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	25.8407	67.6471%	6000000	180000000	1.5164	8.9609%	27.3571	70.5462%	2.8991%
PrimeNet	2⁵⁸	0.0166	62.0690%	10000	190000	0.0019	2.9295%	0.0186	63.1802%	1.1112%
GPU72	2⁶²	0.2663	64.5161%	12000	200000	0.0022	1.7385%	0.2685	65.1330%	0.6169%
Difference	+6	+25.5744	+3.1309%	+5988000	+179800000	+1.5142	+7.2224%	+27.0885	+5.4131%	+5.4131%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

25.8407

67.6471%

6000000

180000000

1.5164

8.9609%

27.3571

70.5462%

2.8991%

PrimeNet

2⁵⁸

0.0166

62.0690%

10000

190000

0.0019

2.9295%

0.0186

63.1802%

1.1112%

GPU72

2⁶²

0.2663

64.5161%

12000

200000

0.0022

1.7385%

0.2685

65.1330%

0.6169%

Difference

+25.5744

+3.1309%

+5988000

+179800000

+1.5142

+7.2224%

+27.0885

+5.4131%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2306627	924073201820696538087791	24	79.612	200308329396277885 5 × 17 × 149 × 1153 × 13717169573	2020-07-22	1153	13717169573	85,076	73.207	136.73

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2306627

924073201820696538087791

79.612

200308329396277885
5 × 17 × 149 × 1153 × 13717169573

2020-07-22

1153

13717169573

85,076

73.207

136.73

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2003-09-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.230%
2010-02-15T08:09:00	Bud	annan	500000	10000000		-		-	-	0.100	-	-	4.371%
2017-12-26T00:23:19	Sid & Andy	Hand_In_The_Box	6000000	180000000	12	-		-	-	1.516	-	-	8.961%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2003-09-14T00:00:00

ANONYMOUS

v4_computers

2048

204800

0.001

-

-

0.230%

2010-02-15T08:09:00

Bud

annan

500000

10000000

0.100

-

-

4.371%

2017-12-26T00:23:19

Sid & Andy

Hand_In_The_Box

6000000

180000000

1.516

-

-

8.961%

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	-	-
2009-01-15T03:21:00	Sturle Sunde	akerman.ifi	2⁶⁰	2⁶¹		-	-	0.067	-	-
2012-05-13T15:33:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.133	-	-
2013-12-06T02:46:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.426	-	-
2015-03-03T21:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.851	-	-
2015-03-03T21:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.620	-	-
2015-10-22T10:17:23	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.240	-	-
2017-05-31T02:32:34	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.479	-	-
2019-05-06T12:23:28	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.96	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.993 GHz-days
Estimated T-Level:	3.950

Digits	B1	Curves	Complete	FacMiss
20	11000	79 / 100	0.790	45.204%
25	50000	79 / 280	0.282	75.379%

New Calculation Method

Total ECM effort:	6.993 GHz-days
Estimated T-Level:	3.950

Digits	B1	Complete	FacMiss
20	11000	2.548	7.821%
25	50000	0.230	79.428%
30	250000	0.014	98.592%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		78	6.905
50000	5000000	924073201820696538087791	1	0.089

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-14T18:04:00	tbw1h	tbw1h03	50000	5000000						3	0.266
2010-01-11T07:14:00	KAMCOBILL	PC01	50000	5000000						3	0.266
2011-12-19T14:16:00	Lukasz Wrobel	i-1	50000	5000000						3	0.266
2013-09-30T23:21:00	Kripke	Kripke	50000	5000000						3	0.266
2015-04-15T08:34:00	Jason U	Server7	50000	5000000						3	0.266
2016-02-14T21:43:55	Sintax	cloud2	50000	5000000						3	0.266
2016-04-26T17:36:21	cherridge	Home	50000	5000000						3	0.266
2016-08-08T12:06:31	Bruce	Desk6	50000	5000000						3	0.266
2017-01-11T16:26:10	Bruce	Desk6	50000	5000000						3	0.266
2017-08-26T02:44:24	Bruce	Desk6	50000	5000000						3	0.266
2018-01-24T02:07:25	Bruce	Desk6	50000	5000000						3	0.266
2018-07-19T08:00:47	Bruce	Desk6	50000	5000000						3	0.266
2019-10-18T12:41:21	monsted	rootweiler	50000	5000000						3	0.266
2020-03-08T15:21:24	Keysarecool	HPLaptop	50000	5000000						3	0.266
2020-03-16T13:11:12	mnd9	75211backdoorb	50000	5000000						3	0.266
2020-03-25T14:03:52	MarkS	laptop64	50000	5000000						3	0.266
2020-04-06T16:38:08	mnd9	eileen	50000	5000000						3	0.266
2020-04-20T13:57:41	Keysarecool	Boat_Anchor	50000	5000000						3	0.266
2020-04-28T09:59:20	Oliver Kruse	Melissa	50000	5000000						3	0.266
2020-05-08T07:27:02	nordi	sweet16	50000	5000000						3	0.266
2020-05-22T06:24:22	mnd9	libproj	50000	5000000						3	0.266
2020-06-09T23:13:25	GAN	OSK-SCH03	50000	5000000						3	0.266
2020-06-25T13:20:03	daveward2005	Davy	50000	5000000						3	0.266
2020-07-03T15:05:48	GAN	LMS-08	50000	5000000						3	0.266
2020-07-10T17:12:11	Leo Custodio	G1-PRIME96-01	50000	5000000						3	0.266
2020-07-15T23:23:02	GAN	LMS-02	50000	5000000						3	0.266
2020-07-22T05:33:28	GAN	LMS-12	50000	5000000	924073201820696538087791	79.612	1	2	6299933176907601	1	0.089

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	988FDE0B0E731C8E	0.156
2018-05-02T02:47:45	kkmrkkblmbrbk	old	988FDE0B0E731C8E	0.156

date

userid

compid

res64

spent (GHz-days)

1999-03-15T00:00:00

ANONYMOUS

v4_computers

988FDE0B0E731C8E

0.156

2018-05-02T02:47:45

kkmrkkblmbrbk

old

988FDE0B0E731C8E

0.156

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 = 6000000, B2 = 180000000 (P-1 stage 2)

B1 = 6000000 (P-1 stage 1)

B1 = 500000, B2 = 10000000 (P-1 stage 2)

B1 = 500000 (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

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