M2947897 Mersenne number exponent details

Residue

Status

L-L

34A842F9BD74C2B3

double-checked

PRP

B2C3CED6AD594F44

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	20.2195	67.6471%	1000000	20000000	0.2512	5.5433%	20.4706	69.4405%	1.7934%
PrimeNet	2⁵⁹	0.0261	62.7119%	13000	260000	0.0033	3.0732%	0.0293	63.8578%	1.1460%
GPU72	2⁶³	0.5414	65.0794%	17000	300000	0.0040	1.9473%	0.5454	65.7594%	0.6800%
Difference	+5	+19.6780	+2.5677%	+983000	+19700000	+0.2472	+3.5959%	+19.9252	+3.6811%	+3.6811%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

20.2195

67.6471%

1000000

20000000

0.2512

5.5433%

20.4706

69.4405%

1.7934%

PrimeNet

2⁵⁹

0.0261

62.7119%

13000

260000

0.0033

3.0732%

0.0293

63.8578%

1.1460%

GPU72

2⁶³

0.5414

65.0794%

17000

300000

0.0040

1.9473%

0.5454

65.7594%

0.6800%

Difference

+19.6780

+2.5677%

+983000

+19700000

+0.2472

+3.5959%

+19.9252

+3.6811%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2947897	5874138399763516739113	22	72.315	996326940826548 2² × 3² × 17 × 29 × 56137420601	2020-10-20	29	56137420601	353.07	377.46	704.98

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2947897

5874138399763516739113

72.315

996326940826548
2² × 3² × 17 × 29 × 56137420601

2020-10-20

56137420601

353.07

377.46

704.98

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	-	-	0.246%
2010-11-04T05:42:00	markr	tiny	95000	1971250		-		-	-	0.024	-	-	2.449%
2014-11-06T23:05:00	Jocelyn Larouche	Manual testing	116773	116773		-		-	-	0.014	-	-	0.928%
2015-04-30T21:53:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.251	-	-	5.543%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:25	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.052	-	-
2009-02-13T21:01:00	Sturle Sunde	bach.ifi	2⁶⁰	2⁶¹		-	-	0.052	-	-
2011-12-14T05:25:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.104	-	-
2013-01-10T21:10:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.333	-	-
2015-04-27T09:54:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.666	-	-
2015-04-27T09:54:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.267	-	-
2016-02-25T09:22:06	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.535	-	-
2017-11-28T10:01:36	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.070	-	-
2018-12-24T00:53:32	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.14	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.126 GHz-days
Estimated T-Level:	1.350

Digits	B1	Curves	Complete	FacMiss
20	11000	27 / 100	0.270	76.234%
25	50000	27 / 280	0.096	90.792%

New Calculation Method

Total ECM effort:	3.126 GHz-days
Estimated T-Level:	1.350

Digits	B1	Complete	FacMiss
20	11000	0.871	41.855%
25	50000	0.079	92.430%
30	250000	0.005	99.516%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		25	2.895
50000	5000000	5874138399763516739113	2	0.232

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-03T15:01:00	CPSlacker	bf-st-2k3-1P	50000	5000000						3	0.347
2011-04-25T11:14:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.347
2013-07-04T04:19:00	Bruce	fx6840-21	50000	5000000						3	0.347
2016-01-01T09:55:27	Bruce	Desk7	50000	5000000						3	0.347
2017-06-03T05:23:22	ANONYMOUS	HP-Z220-CMT	50000	5000000						3	0.347
2019-10-03T04:20:31	Claude Portenier	Petit-Idiot	50000	5000000						3	0.347
2020-09-14T13:48:47	rextherunt	ice	50000	5000000						7	0.811
2020-10-20T23:22:29	mnd9	kitchen	50000	5000000	5874138399763516739113	72.315	2	2	7992276033563842	2	0.232

date	userid	compid	res64	spent (GHz-days)
1999-05-09T00:00:00	ANONYMOUS	v4_computers	34A842F9BD74C2B3	0.251
2018-10-12T03:56:25	kkmrkkblmbrbk	old	34A842F9BD74C2B3	0.251

date

userid

compid

res64

spent (GHz-days)

1999-05-09T00:00:00

ANONYMOUS

v4_computers

34A842F9BD74C2B3

0.251

2018-10-12T03:56:25

kkmrkkblmbrbk

old

34A842F9BD74C2B3

0.251

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 = 1971250 (P-1 stage 2)

B1 = 116773 (P-1 stage 1)

B1 = 95000 (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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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