M2347727 Mersenne number exponent details

Residue

Status

L-L

CD3FCB35DBBCA2CE

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	25.3883	67.6471%	6000000	180000000	1.5164	8.9754%	26.9047	70.5509%	2.9038%
PrimeNet	2⁵⁸	0.0164	62.0690%	11000	200000	0.0021	3.0481%	0.0184	63.2252%	1.1562%
GPU72	2⁶²	0.2617	64.5161%	13000	220000	0.0024	1.8352%	0.2641	65.1673%	0.6512%
Difference	+6	+25.1267	+3.1309%	+5987000	+179780000	+1.5140	+7.1402%	+26.6406	+5.3835%	+5.3835%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

25.3883

67.6471%

6000000

180000000

1.5164

8.9754%

26.9047

70.5509%

2.9038%

PrimeNet

2⁵⁸

0.0164

62.0690%

11000

200000

0.0021

3.0481%

0.0184

63.2252%

1.1562%

GPU72

2⁶²

0.2617

64.5161%

13000

220000

0.0024

1.8352%

0.2641

65.1673%

0.6512%

Difference

+25.1267

+3.1309%

+5987000

+179780000

+1.5140

+7.1402%

+26.6406

+5.3835%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2347727	4496588157403708353609793	25	81.895	957647153481582048 2⁵ × 3 × 9975491182099813	2020-06-22	32	9975491182099813	227,021	53,238,088	99,433,923

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2347727

4496588157403708353609793

81.895

957647153481582048
2⁵ × 3 × 9975491182099813

2020-06-22

9975491182099813

227,021

53,238,088

99,433,923

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2003-09-21T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.231%
2010-03-05T07:43:00	Bud	annan	500000	10000000		-		-	-	0.100	-	-	4.381%
2018-01-30T13:30:15	Sid & Andy	Hand_In_The_Box	6000000	180000000	12	-		-	-	1.516	-	-	8.975%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2003-09-21T00:00:00

ANONYMOUS

v4_computers

2048

204800

0.001

-

-

0.231%

2010-03-05T07:43:00

Bud

annan

500000

10000000

0.100

-

-

4.381%

2018-01-30T13:30:15

Sid & Andy

Hand_In_The_Box

6000000

180000000

1.516

-

-

8.975%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:12	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.065	-	-
2009-01-16T00:14:00	Sturle Sunde	celair.ifi	2⁶⁰	2⁶¹		-	-	0.065	-	-
2012-05-29T11:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.131	-	-
2013-12-04T21:14:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.418	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.836	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.591	-	-
2015-10-27T09:37:24	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.183	-	-
2017-06-11T03:38:01	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.366	-	-
2019-03-04T13:44:33	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.73	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.413 GHz-days
Estimated T-Level:	3.050

Digits	B1	Curves	Complete	FacMiss
20	11000	61 / 100	0.610	54.169%
25	50000	61 / 280	0.218	80.393%

New Calculation Method

Total ECM effort:	5.413 GHz-days
Estimated T-Level:	3.050

Digits	B1	Complete	FacMiss
20	11000	1.968	13.977%
25	50000	0.178	83.707%
30	250000	0.011	98.911%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		60	5.324
50000	5000000	4496588157403708353609793	1	0.089

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-25T18:31:00	Luigi Morelli	AMD64x2	50000	5000000						3	0.266
2010-01-27T18:51:00	SubPrime	abd0	50000	5000000						3	0.266
2011-12-23T17:57:00	S36049	Wolle5	50000	5000000						3	0.266
2013-11-04T12:45:00	Lukasz Wrobel	i-1	50000	5000000						3	0.266
2015-06-07T18:44:00	dragon325	Falken-i7-920	50000	5000000						3	0.266
2016-02-17T14:41:08	Sintax	cloud	50000	5000000						3	0.266
2016-05-08T08:11:10	Bruce	Desk6	50000	5000000						3	0.266
2016-08-29T06:18:12	Bruce	Desk6	50000	5000000						3	0.266
2017-02-24T20:21:42	Bruce	Desk6	50000	5000000						3	0.266
2017-09-27T10:28:53	Bruce	Desk6	50000	5000000						3	0.266
2018-02-24T23:37:57	Bruce	Desk6	50000	5000000						3	0.266
2018-08-20T17:32:49	Bruce	Desk6	50000	5000000						3	0.266
2020-03-15T10:12:49	Janneman	JanP03	50000	5000000						3	0.266
2020-03-21T22:11:40	IanGlencross	glenx24	50000	5000000						3	0.266
2020-04-04T08:26:09	IanGlencross	glenx24	50000	5000000						3	0.266
2020-04-17T15:40:07	Sergey Nosov	TS140-02	50000	5000000						3	0.266
2020-04-28T03:30:49	Claude Portenier	Petit-Idiot	50000	5000000						3	0.266
2020-05-05T04:51:48	mnd9	libproj	50000	5000000						3	0.266
2020-05-16T10:58:57	Keysarecool	HPLaptop	50000	5000000						3	0.266
2020-06-04T14:28:09	Loic	workstation	50000	5000000						3	0.266
2020-06-22T10:10:42	mnd9	office2	50000	5000000	4496588157403708353609793	81.895	1	2	2852933347243976	1	0.089

date	userid	compid	res64	spent (GHz-days)
1999-03-01T00:00:00	ANONYMOUS	v4_computers	CD3FCB35DBBCA2CE	0.159

date

userid

compid

res64

spent (GHz-days)

1999-03-01T00:00:00

ANONYMOUS

v4_computers

CD3FCB35DBBCA2CE

0.159

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

10¹⁶

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