M2972029 Mersenne number exponent details

Residue

Status

L-L

151DDF53434BF5C7

double-checked

PRP

60CE92B5D21124FD

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	2⁶⁹	40.1701	68.1159%	1000000	20000000	0.2512	5.0599%	40.4213	69.7293%	1.6133%
PrimeNet	2⁶⁰	0.0517	63.3333%	12000	220000	0.0029	2.5108%	0.0546	64.2539%	0.9206%
GPU72	2⁶⁴	1.1976	65.6250%	12000	200000	0.0027	1.3487%	1.2004	66.0886%	0.4636%
Difference	+5	+38.9725	+2.4909%	+988000	+19800000	+0.2484	+3.7113%	+39.2209	+3.6407%	+3.6407%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

40.1701

68.1159%

1000000

20000000

0.2512

5.0599%

40.4213

69.7293%

1.6133%

PrimeNet

2⁶⁰

0.0517

63.3333%

12000

220000

0.0029

2.5108%

0.0546

64.2539%

0.9206%

GPU72

2⁶⁴

1.1976

65.6250%

12000

200000

0.0027

1.3487%

1.2004

66.0886%

0.4636%

Difference

+38.9725

+2.4909%

+988000

+19800000

+0.2484

+3.7113%

+39.2209

+3.6407%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2972029	754666415612671667177	21	69.354	126961482477572 2² × 470059 × 67524227	2021-05-28	470059	67524227	44.628	0.5089	0.8480

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2972029

754666415612671667177

69.354

126961482477572
2² × 470059 × 67524227

2021-05-28

470059

67524227

44.628

0.5089

0.8480

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	-	-	0.199%
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.120%
2010-10-27T19:04:00	markr	tiny	95000	1995000		-		-	-	0.024	-	-	2.180%
2015-05-08T13:54:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.251	-	-	5.060%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.052	-	-
2009-02-12T23:52:00	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		-	-	2.514	-	-
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	-	-
2021-05-17T10:42:34	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	20.11	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.344 GHz-days
Estimated T-Level:	3.550

Digits	B1	Curves	Complete	FacMiss
20	11000	71 / 100	0.710	48.989%
25	50000	71 / 280	0.254	77.567%

New Calculation Method

Total ECM effort:	8.344 GHz-days
Estimated T-Level:	3.550

Digits	B1	Complete	FacMiss
20	11000	2.306	9.967%
25	50000	0.208	81.183%
30	250000	0.013	98.724%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		60	6.957
50000	5000000	754666415612671667177	4	0.464
50000	6570567		7	0.923

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-01T08:37:00	James Hintz	14_060209	50000	5000000						3	0.348
2011-05-02T08:28:00	sannerud.com	Jim2010	50000	5000000						3	0.348
2013-07-25T09:25:00	Bruce	fx6840-21	50000	5000000						3	0.348
2016-01-08T05:37:33	Bruce	Desk7	50000	5000000						3	0.348
2017-06-24T10:19:28	bayanne	iMac	50000	5000000						3	0.348
2019-11-11T12:03:03	mnd9	75204	50000	5000000						3	0.348
2020-09-15T21:42:28	GAN	OSB-02	50000	5000000						7	0.812
2020-10-17T08:52:16	GAN	AC-GR	50000	5000000						7	0.812
2020-11-18T01:04:36	MarkS	laptop64	50000	5000000						7	0.812
2020-12-27T00:05:12	rextherunt	ice	50000	5000000						7	0.812
2021-01-25T07:33:39	Zenzoma	AMD3970X	50000	5000000						7	0.812
2021-02-23T19:55:22	lycorn	colab_S_2	50000	6570567						7	0.923
2021-03-31T14:13:08	mnd9	kitchen	50000	5000000						7	0.812
2021-05-28T10:58:04	daveward2005	Dave2	50000	5000000	754666415612671667177	69.354	4	2	631462294202522	4	0.464

date	userid	compid	res64	spent (GHz-days)
1998-01-16T00:00:00	ANONYMOUS	v4_computers	151DDF53434BF5C7	0.253
1999-05-23T00:00:00	ANONYMOUS	v4_computers	151DDF53434BF5C7	0.253
2018-10-18T05:34:34	kkmrkkblmbrbk	old	151DDF53434BF5C7	0.253

date

userid

compid

res64

spent (GHz-days)

1998-01-16T00:00:00

ANONYMOUS

v4_computers

151DDF53434BF5C7

0.253

1999-05-23T00:00:00

ANONYMOUS

v4_computers

151DDF53434BF5C7

0.253

2018-10-18T05:34:34

kkmrkkblmbrbk

old

151DDF53434BF5C7

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)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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