M2947999 Mersenne number exponent details

Residue

Status

L-L

3334DA7A5A602F39

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	2⁶⁷	10.0794	67.1642%	1000000	20000000	0.2512	6.0731%	10.3305	69.1583%	1.9942%
PrimeNet	2⁵⁹	0.0260	62.7119%	13000	260000	0.0033	3.0733%	0.0293	63.8578%	1.1460%
GPU72	2⁶³	0.5414	65.0794%	17000	300000	0.0040	1.9474%	0.5454	65.7594%	0.6800%
Difference	+4	+9.5380	+2.0848%	+983000	+19700000	+0.2472	+4.1258%	+9.7851	+3.3989%	+3.3989%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

10.0794

67.1642%

1000000

20000000

0.2512

6.0731%

10.3305

69.1583%

1.9942%

PrimeNet

2⁵⁹

0.0260

62.7119%

13000

260000

0.0033

3.0733%

0.0293

63.8578%

1.1460%

GPU72

2⁶³

0.5414

65.0794%

17000

300000

0.0040

1.9474%

0.5454

65.7594%

0.6800%

Difference

+9.5380

+2.0848%

+983000

+19700000

+0.2472

+4.1258%

+9.7851

+3.3989%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2947999	185961933971661264563017	24	77.299	31540365850134492 2² × 3² × 13 × 67393944124219	2016-01-01	13	67393944124219	16,882	453,142	846,343

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2947999

185961933971661264563017

77.299

31540365850134492
2² × 3² × 13 × 67393944124219

2016-01-01

67393944124219

16,882

453,142

846,343

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	-	-	0.305%
2010-11-04T05:05:00	markr	tiny	95000	1971250		-		-	-	0.024	-	-	2.758%
2014-11-06T23:05:00	Jocelyn Larouche	Manual testing	116772	116772		-		-	-	0.014	-	-	1.066%
2015-04-30T21:53:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.251	-	-	6.073%

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	-	-
2009-02-13T21:45:00	Sturle Sunde	bach.ifi	2⁶⁰	2⁶¹		-	-	0.052	-	-
2011-07-16T12:28:00	Rob_Dee	twopc	2⁶¹	2⁶²		-	-	0.104	-	-
2013-01-07T13:49:00	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	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.274 GHz-days
Estimated T-Level:	0.550

Digits	B1	Curves	Complete	FacMiss
20	11000	11 / 100	0.110	89.534%
25	50000	11 / 280	0.039	96.141%

New Calculation Method

Total ECM effort:	1.274 GHz-days
Estimated T-Level:	0.550

Digits	B1	Complete	FacMiss
20	11000	0.355	70.129%
25	50000	0.032	96.844%
30	250000	0.002	99.803%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.042
50000	5000000	185961933971661264563017	2	0.232

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-11-06T19:07:00	James Classen	towerofart	50000	5000000						3	0.347
2011-04-18T09:03:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.347
2013-07-04T07:05:00	Bruce	fx6840-21	50000	5000000						3	0.347
2016-01-01T09:14:04	Bruce	Desk7	50000	5000000	185961933971661264563017	77.299	2	2		2	0.232

date	userid	compid	res64	spent (GHz-days)
1999-08-22T00:00:00	ANONYMOUS	v4_computers	3334DA7A5A602F39	0.251

date

userid

compid

res64

spent (GHz-days)

1999-08-22T00:00:00

ANONYMOUS

v4_computers

3334DA7A5A602F39

0.251

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:32:47

alpertron

Manual testing

185961933971661264563017

32105DCC840415__

2017-11-18T09:59:55

Oliver Kruse

GTX-2

185961933971661264563017

32105DCC840415__

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 = 116772 (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

10¹²

10¹³

10¹⁴

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