M2319353 Mersenne number exponent details

Residue

Status

L-L

A21C46F67AE41E06

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	25.6989	67.6471%	6000000	180000000	1.5164	8.9654%	27.2153	70.5476%	2.9006%
PrimeNet	2⁵⁸	0.0166	62.0690%	10000	190000	0.0019	2.9325%	0.0185	63.1813%	1.1123%
GPU72	2⁶²	0.2649	64.5161%	13000	200000	0.0023	1.7819%	0.2672	65.1484%	0.6323%
Difference	+6	+25.4340	+3.1309%	+5987000	+179800000	+1.5141	+7.1835%	+26.9481	+5.3992%	+5.3992%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

25.6989

67.6471%

6000000

180000000

1.5164

8.9654%

27.2153

70.5476%

2.9006%

PrimeNet

2⁵⁸

0.0166

62.0690%

10000

190000

0.0019

2.9325%

0.0185

63.1813%

1.1123%

GPU72

2⁶²

0.2649

64.5161%

13000

200000

0.0023

1.7819%

0.2672

65.1484%

0.6323%

Difference

+25.4340

+3.1309%

+5987000

+179800000

+1.5141

+7.1835%

+26.9481

+5.3992%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2319353	23131465349852264601193	23	74.292	4986620266482132 2² × 3 × 415551688873511	2020-08-02	4	415551688873511	1,803.8	2,217,753	4,142,145

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2319353

23131465349852264601193

74.292

4986620266482132
2² × 3 × 415551688873511

2020-08-02

415551688873511

1,803.8

2,217,753

4,142,145

	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%
2010-02-22T08:15:00	Bud	annan	500000	10000000		-		-	-	0.100	-	-	4.374%
2018-01-20T09:54:48	Sid & Andy	Hand_In_The_Box	6000000	180000000	12	-		-	-	1.516	-	-	8.965%

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%

2010-02-22T08:15:00

Bud

annan

500000

10000000

0.100

-

-

4.374%

2018-01-20T09:54:48

Sid & Andy

Hand_In_The_Box

6000000

180000000

1.516

-

-

8.965%

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	-	-
2009-01-14T05:48:00	Sturle Sunde	giasha.ifi	2⁶⁰	2⁶¹		-	-	0.066	-	-
2012-05-24T14:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.132	-	-
2013-01-23T08:26:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.423	-	-
2015-03-03T21:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.846	-	-
2015-03-03T21:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.611	-	-
2015-10-23T09:34:56	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.222	-	-
2017-06-04T00:25:31	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.444	-	-
2019-04-15T13:43:04	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.89	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.264 GHz-days
Estimated T-Level:	4.100

Digits	B1	Curves	Complete	FacMiss
20	11000	82 / 100	0.820	43.862%
25	50000	82 / 280	0.293	74.574%

New Calculation Method

Total ECM effort:	7.264 GHz-days
Estimated T-Level:	4.100

Digits	B1	Complete	FacMiss
20	11000	2.645	7.099%
25	50000	0.239	78.736%
30	250000	0.015	98.539%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		81	7.176
50000	5000000	23131465349852264601193	1	0.089

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-22T02:18:00	Luigi Morelli	AMD64x2	50000	5000000						3	0.266
2010-01-16T05:13:00	James Classen	towerofart	50000	5000000						3	0.266
2011-12-05T08:59:00	S36049	Wolle5	50000	5000000						3	0.266
2013-10-09T09:48:00	Fretard Loic	Glados	50000	5000000						3	0.266
2015-05-07T15:05:00	Lukasz Wrobel	i-1	50000	5000000						3	0.266
2016-02-15T16:55:50	Sintax	cloud	50000	5000000						3	0.266
2016-04-27T13:12:08	Bruce	Desk6	50000	5000000						3	0.266
2016-08-14T01:59:58	Bruce	Desk6	50000	5000000						3	0.266
2017-01-22T03:55:57	Bruce	Desk6	50000	5000000						3	0.266
2017-09-04T11:59:17	Bruce	Desk6	50000	5000000						3	0.266
2018-02-02T10:20:07	Bruce	Desk6	50000	5000000						3	0.266
2018-07-29T07:54:18	Bruce	Desk6	50000	5000000						3	0.266
2019-11-05T04:54:55	monsted	rootweiler	50000	5000000						3	0.266
2020-03-13T04:40:03	Nesowa	entropy_generator_2	50000	5000000						3	0.266
2020-03-27T04:25:15	cappy95833	HomePC	50000	5000000						3	0.266
2020-03-31T20:38:20	MarkS	desktop-i7	50000	5000000						3	0.266
2020-04-13T23:33:35	mnd9	eileen	50000	5000000						3	0.266
2020-04-24T22:45:42	mnd9	25836b	50000	5000000						3	0.266
2020-05-02T07:46:20	Oliver Kruse	IOS-1	50000	5000000						3	0.266
2020-05-15T10:04:45	Brett Walker	brain	50000	5000000						3	0.266
2020-05-30T16:54:30	mnd9	25836b	50000	5000000						3	0.266
2020-06-22T05:52:29	LaurV	3tits	50000	5000000						3	0.266
2020-06-30T04:58:16	GAN	OSK-01	50000	5000000						3	0.266
2020-07-13T12:13:55	GAN	LMS-07	50000	5000000						3	0.266
2020-07-13T15:27:22	mnd9	office2	50000	5000000						3	0.266
2020-07-19T09:14:14	GAN	OSB-02	50000	5000000						3	0.266
2020-07-26T02:16:22	rextherunt	ice	50000	5000000						3	0.266
2020-08-02T00:35:26	MarkS	desktop-i7	50000	5000000	23131465349852264601193	74.292	1	2	5971126826608546	1	0.089

date	userid	compid	res64	spent (GHz-days)
2015-11-15T02:09:49	MadPoo	Manual testing	A21C46F67AE41E06	0.157

date

userid

compid

res64

spent (GHz-days)

2015-11-15T02:09:49

MadPoo

Manual testing

A21C46F67AE41E06

0.157

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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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