M2314709 Mersenne number exponent details

Residue

Status

L-L

FDBFA8FA60B4E968

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	25.7505	67.6471%	6000000	180000000	1.5164	8.9638%	27.2668	70.5471%	2.9000%
PrimeNet	2⁵⁸	0.0166	62.0690%	10000	190000	0.0019	2.9314%	0.0185	63.1809%	1.1119%
GPU72	2⁶²	0.2654	64.5161%	13000	200000	0.0023	1.7812%	0.2677	65.1482%	0.6320%
Difference	+6	+25.4851	+3.1309%	+5987000	+179800000	+1.5141	+7.1825%	+26.9991	+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

25.7505

67.6471%

6000000

180000000

1.5164

8.9638%

27.2668

70.5471%

2.9000%

PrimeNet

2⁵⁸

0.0166

62.0690%

10000

190000

0.0019

2.9314%

0.0185

63.1809%

1.1119%

GPU72

2⁶²

0.2654

64.5161%

13000

200000

0.0023

1.7812%

0.2677

65.1482%

0.6320%

Difference

+25.4851

+3.1309%

+5987000

+179800000

+1.5141

+7.1825%

+26.9991

+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
2314709	5320595040520597410336296657	28	92.104	1149301065602759873992 2³ × 17 × 677 × 83768947 × 149012663	2020-08-08	83768947	149012663	826,467,642	8.5538	16.700

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2314709

5320595040520597410336296657

92.104

1149301065602759873992
2³ × 17 × 677 × 83768947 × 149012663

2020-08-08

83768947

149012663

826,467,642

8.5538

16.700

	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%
2018-01-09T19:26:41	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%

2018-01-09T19:26:41

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
2016-02-23T16:29:11	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.066	-	-
2009-01-17T13:51:00	Sturle Sunde	nouchcraft.ifi	2⁶⁰	2⁶¹		-	-	0.066	-	-
2012-05-23T18:44:00	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		-	-	1.614	-	-
2015-10-23T09:34:55	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.228	-	-
2017-06-04T00:25:30	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.457	-	-
2019-04-22T13:11:36	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.91	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.617 GHz-days
Estimated T-Level:	4.300

Digits	B1	Curves	Complete	FacMiss
20	11000	86 / 100	0.860	42.133%
25	50000	86 / 280	0.307	73.514%

New Calculation Method

Total ECM effort:	7.617 GHz-days
Estimated T-Level:	4.300

Digits	B1	Complete	FacMiss
20	11000	2.774	6.240%
25	50000	0.251	77.823%
30	250000	0.015	98.468%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		84	7.439
50000	5000000	5320595040520597410336296657	2	0.177

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-19T13:13:00	Smurgs	Praca	50000	5000000						3	0.266
2010-01-14T08:33:00	James Classen	towerofart	50000	5000000						3	0.266
2011-12-01T20:20:00	Wojciech Florek	gafel	50000	5000000						3	0.266
2013-10-06T07:03:00	Bruce	apandya-DESK11	50000	5000000						3	0.266
2015-04-25T17:21:00	dragon325	Falken-i7-920	50000	5000000						3	0.266
2016-02-15T13:29:55	Sintax	cloud	50000	5000000						3	0.266
2016-04-26T05:39:54	Bruce	Desk6	50000	5000000						3	0.266
2016-08-12T06:41:46	Bruce	Desk6	50000	5000000						3	0.266
2017-01-17T19:45:13	Bruce	Desk6	50000	5000000						3	0.266
2017-09-01T04:45:03	Bruce	Desk6	50000	5000000						3	0.266
2018-01-30T08:17:04	Bruce	Desk6	50000	5000000						3	0.266
2018-07-24T21:31:46	Bruce	Desk6	50000	5000000						3	0.266
2019-10-28T06:19:03	monsted	rootweiler	50000	5000000						3	0.266
2020-03-11T06:38:03	mnd9	25836b	50000	5000000						3	0.266
2020-03-18T22:55:45	Brett Walker	brain	50000	5000000						3	0.266
2020-03-30T09:35:27	daveward2005	MW	50000	5000000						3	0.266
2020-04-11T05:19:00	Oliver Kruse	IOS-1	50000	5000000						3	0.266
2020-04-23T06:39:36	nordi	sweet16	50000	5000000						3	0.266
2020-04-30T20:41:57	mnd9	27016b	50000	5000000						3	0.266
2020-05-11T14:34:28	mnd9	eileen	50000	5000000						3	0.266
2020-05-26T12:56:18	Summy	CHB	50000	5000000						3	0.266
2020-06-15T03:39:53	daveward2005	Davy	50000	5000000						3	0.266
2020-06-29T10:15:50	LaurV	3tits	50000	5000000						3	0.266
2020-07-05T16:55:30	GAN	LMS-08	50000	5000000						3	0.266
2020-07-12T05:29:53	GAN	LMS-11	50000	5000000						3	0.266
2020-07-18T02:07:57	GAN	LMS-06	50000	5000000						3	0.266
2020-07-24T04:28:59	gLauss	laptop-klaus	50000	5000000						3	0.266
2020-07-31T11:02:26	daveward2005	Dave2	50000	5000000						3	0.266
2020-08-08T00:11:18	GAN	LMS-06	50000	5000000	5320595040520597410336296657	92.104	2	2	956099628029880	2	0.177

date	userid	compid	res64	spent (GHz-days)
1999-03-01T00:00:00	ANONYMOUS	v4_computers	FDBFA8FA60B4E968	0.156
2018-05-04T04:07:07	kkmrkkblmbrbk	old	FDBFA8FA60B4E968	0.156

date

userid

compid

res64

spent (GHz-days)

1999-03-01T00:00:00

ANONYMOUS

v4_computers

FDBFA8FA60B4E968

0.156

2018-05-04T04:07:07

kkmrkkblmbrbk

old

FDBFA8FA60B4E968

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

10⁸

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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