M2971747 Mersenne number exponent details

Residue

Status

L-L

A74802729676A751

double-checked

PRP

99EAA064CF616863

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	20.0572	67.6471%	1000000	20000000	0.2512	5.5483%	20.3083	69.4421%	1.7951%
PrimeNet	2⁶⁰	0.0517	63.3333%	12000	220000	0.0029	2.5107%	0.0546	64.2539%	0.9206%
GPU72	2⁶⁴	1.1977	65.6250%	12000	200000	0.0027	1.3486%	1.2005	66.0886%	0.4636%
Difference	+4	+18.8595	+2.0221%	+988000	+19800000	+0.2484	+4.1997%	+19.1079	+3.3535%	+3.3535%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

20.0572

67.6471%

1000000

20000000

0.2512

5.5483%

20.3083

69.4421%

1.7951%

PrimeNet

2⁶⁰

0.0517

63.3333%

12000

220000

0.0029

2.5107%

0.0546

64.2539%

0.9206%

GPU72

2⁶⁴

1.1977

65.6250%

12000

200000

0.0027

1.3486%

1.2005

66.0886%

0.4636%

Difference

+18.8595

+2.0221%

+988000

+19800000

+0.2484

+4.1997%

+19.1079

+3.3535%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2971747	135424165284173204965439	24	76.842	22785278370630677 11 × 53 × 349 × 367 × 305136593	2020-11-17	367	305136593	7,442.8	2.0517	3.8319

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2971747

135424165284173204965439

76.842

22785278370630677
11 × 53 × 349 × 367 × 305136593

2020-11-17

367

305136593

7,442.8

2.0517

3.8319

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-13T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.247%
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.146%
2010-10-27T20:58:00	markr	tiny	95000	1995000		-		-	-	0.024	-	-	2.459%
2015-05-08T13:54:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.251	-	-	5.548%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-02T00:00:00	Nayan Hajratwala	v4_computers	2¹	2⁶⁰		-	-	0.052	-	-
2009-02-12T22:01:00	Sturle Sunde	antonov.ifi	2⁶⁰	2⁶¹		-	-	0.052	-	-
2011-11-29T06:57:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.103	-	-
2013-01-07T13:51:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.330	-	-
2015-04-29T14:58:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.661	-	-
2015-04-29T14:58:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.257	-	-
2016-02-28T22:17:41	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.515	-	-
2017-12-03T16:23:23	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.029	-	-
2018-12-25T13:40:43	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.06	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.174 GHz-days
Estimated T-Level:	1.800

Digits	B1	Curves	Complete	FacMiss
20	11000	36 / 100	0.360	69.641%
25	50000	36 / 280	0.129	87.915%

New Calculation Method

Total ECM effort:	4.174 GHz-days
Estimated T-Level:	1.800

Digits	B1	Complete	FacMiss
20	11000	1.161	31.308%
25	50000	0.105	90.036%
30	250000	0.006	99.356%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		32	3.710
50000	5000000	135424165284173204965439	4	0.464

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-01T15:41:00	James Hintz	19_060209	50000	5000000						3	0.348
2011-05-04T15:47:00	Pool Party	desk_1	50000	5000000						3	0.348
2013-07-25T04:57:00	Bruce	fx6840-21	50000	5000000						3	0.348
2016-01-08T03:40:06	Bruce	Desk7	50000	5000000						3	0.348
2017-06-27T17:57:45	Lelikoid	QH	50000	5000000						3	0.348
2019-11-12T02:49:01	Claude Portenier	Petit-Idiot	50000	5000000						3	0.348
2020-09-17T15:02:33	rextherunt	ice	50000	5000000						7	0.812
2020-10-17T06:45:10	Gerry Snyder	Gerry-Workstation	50000	5000000						7	0.812
2020-11-17T23:51:28	MarkS	laptop64	50000	5000000	135424165284173204965439	76.842	4	2	6802401106540666	4	0.464

date	userid	compid	res64	spent (GHz-days)
1999-06-15T00:00:00	Nayan Hajratwala	v4_computers	A74802729676A751	0.253
2018-10-18T04:12:56	kkmrkkblmbrbk	old	A74802729676A751	0.253

date

userid

compid

res64

spent (GHz-days)

1999-06-15T00:00:00

Nayan Hajratwala

v4_computers

A74802729676A751

0.253

2018-10-18T04:12:56

kkmrkkblmbrbk

old

A74802729676A751

0.253

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 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 95000, B2 = 1995000 (P-1 stage 2)

B1 = 95000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

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