M2314253 Mersenne number exponent details

Residue

Status

L-L

D8B538786EACDBEF

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	25.7556	67.6471%	6000000	180000000	1.5164	8.9636%	27.2719	70.5470%	2.9000%
PrimeNet	2⁵⁸	0.0166	62.0690%	10000	190000	0.0019	2.9313%	0.0185	63.1808%	1.1119%
GPU72	2⁶²	0.2655	64.5161%	13000	200000	0.0023	1.7811%	0.2677	65.1481%	0.6320%
Difference	+6	+25.4901	+3.1309%	+5987000	+179800000	+1.5141	+7.1825%	+27.0042	+5.3989%	+5.3989%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

25.7556

67.6471%

6000000

180000000

1.5164

8.9636%

27.2719

70.5470%

2.9000%

PrimeNet

2⁵⁸

0.0166

62.0690%

10000

190000

0.0019

2.9313%

0.0185

63.1808%

1.1119%

GPU72

2⁶²

0.2655

64.5161%

13000

200000

0.0023

1.7811%

0.2677

65.1481%

0.6320%

Difference

+25.4901

+3.1309%

+5987000

+179800000

+1.5141

+7.1825%

+27.0042

+5.3989%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2314253	96959036775739694748223	23	76.360	20948236164269787 3 × 41647 × 167665027207	2020-07-05	41647	167665027207	9,571.6	894.81	1,671.3

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2314253

96959036775739694748223

76.360

20948236164269787
3 × 41647 × 167665027207

2020-07-05

41647

167665027207

9,571.6

894.81

1,671.3

	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%
2010-02-16T08:20:00	Bud	annan	500000	10000000		-		-	-	0.100	-	-	4.373%
2018-01-10T05:46:01	Sid & Andy	Hand_In_The_Box	6000000	180000000	12	-		-	-	1.516	-	-	8.964%

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%

2010-02-16T08:20:00

Bud

annan

500000

10000000

0.100

-

-

4.373%

2018-01-10T05:46:01

Sid & Andy

Hand_In_The_Box

6000000

180000000

1.516

-

-

8.964%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.017	-	-
2016-02-23T16:29:11	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.050	-	-
2009-01-17T11:30:00	Sturle Sunde	nouchcraft.ifi	2⁶⁰	2⁶¹		-	-	0.066	-	-
2012-05-23T18:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.133	-	-
2013-12-06T02:47:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.424	-	-
2015-03-03T21:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.848	-	-
2015-03-03T21:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.615	-	-
2015-10-23T09:34:55	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.229	-	-
2017-06-04T00:25:30	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.458	-	-
2019-04-22T13:11:36	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.92	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.199 GHz-days
Estimated T-Level:	3.500

Digits	B1	Curves	Complete	FacMiss
20	11000	70 / 100	0.700	49.484%
25	50000	70 / 280	0.250	77.845%

New Calculation Method

Total ECM effort:	6.199 GHz-days
Estimated T-Level:	3.500

Digits	B1	Complete	FacMiss
20	11000	2.258	10.455%
25	50000	0.204	81.540%
30	250000	0.013	98.751%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		69	6.111
50000	5000000	96959036775739694748223	1	0.089

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-23T00:40:00	SubPrime	c2d0	50000	5000000						3	0.266
2010-01-13T21:41:00	sannerud.com	strs-w2k8e	50000	5000000						3	0.266
2011-12-03T01:06:00	S36049	Wolle5	50000	5000000						3	0.266
2013-10-05T13:54:00	arnaud	srv-630	50000	5000000						3	0.266
2015-04-19T17:20:00	Syntony	Hadfield	50000	5000000						3	0.266
2016-02-15T05:36:10	Sintax	cloud	50000	5000000						3	0.266
2016-04-26T03:29:08	Bruce	Desk6	50000	5000000						3	0.266
2016-08-12T04:01:25	Bruce	Desk6	50000	5000000						3	0.266
2017-01-17T12:58:22	Bruce	Desk6	50000	5000000						3	0.266
2017-08-31T21:57:19	Bruce	Desk6	50000	5000000						3	0.266
2018-01-30T01:41:38	Bruce	Desk6	50000	5000000						3	0.266
2018-07-24T11:51:21	Bruce	Desk6	50000	5000000						3	0.266
2019-10-26T03:30:03	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.266
2020-03-10T18:45:49	Keysarecool	HPLaptop	50000	5000000						3	0.266
2020-03-18T09:41:30	Keysarecool	HPLaptop	50000	5000000						3	0.266
2020-03-29T11:17:55	MarkS	desktop-i7	50000	5000000						3	0.266
2020-04-11T02:42:12	mnd9	libproj	50000	5000000						3	0.266
2020-04-23T09:36:57	nranks	wlaptop	50000	5000000						3	0.266
2020-05-01T02:05:15	mnd9	27016b	50000	5000000						3	0.266
2020-05-11T14:09:05	nordi	sweet16	50000	5000000						3	0.266
2020-05-26T20:27:27	Sergey Nosov	TS140-02	50000	5000000						3	0.266
2020-06-15T06:12:26	daveward2005	MW	50000	5000000						3	0.266
2020-06-28T13:15:39	GAN	LMS-12	50000	5000000						3	0.266
2020-07-05T13:49:56	GAN	LMS-03	50000	5000000	96959036775739694748223	76.360	1	2	4027879029528476	1	0.089

date	userid	compid	res64	spent (GHz-days)
1999-05-23T00:00:00	ANONYMOUS	v4_computers	D8B538786EACDBEF	0.156
2018-05-04T03:10:24	kkmrkkblmbrbk	old	D8B538786EACDBEF	0.156

date

userid

compid

res64

spent (GHz-days)

1999-05-23T00:00:00

ANONYMOUS

v4_computers

D8B538786EACDBEF

0.156

2018-05-04T03:10:24

kkmrkkblmbrbk

old

D8B538786EACDBEF

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

10¹²

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