M7291519 Mersenne number exponent details

Residue

Status

L-L

6A21FEA8E215979A

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	4.0751	65.6716%	90000	1620000	0.0548	2.9869%	4.1299	66.6970%	1.0254%
PrimeNet	2⁶³	0.2189	63.4921%	32000	800000	0.0233	3.3798%	0.2422	64.7260%	1.2339%
GPU72	2⁶⁷	4.0751	65.6716%	45000	1000000	0.0307	2.3153%	4.1058	66.4664%	0.7948%
Difference	-	-	-	+45000	+620000	+0.0241	+0.6716%	+0.0241	+0.2306%	+0.2306%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

4.0751

65.6716%

90000

1620000

0.0548

2.9869%

4.1299

66.6970%

1.0254%

PrimeNet

2⁶³

0.2189

63.4921%

32000

800000

0.0233

3.3798%

0.2422

64.7260%

1.2339%

GPU72

2⁶⁷

4.0751

65.6716%

45000

1000000

0.0307

2.3153%

4.1058

66.4664%

0.7948%

Difference

+45000

+620000

+0.0241

+0.6716%

+0.0241

+0.2306%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
7291519	18628035398037835973393	23	73.980	1277376867428984 2³ × 7² × 539309 × 6042203	2017-12-14	539309	6042203	394.31	0.2653	0.3470

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

7291519

18628035398037835973393

73.980

1277376867428984
2³ × 7² × 539309 × 6042203

2017-12-14

539309

6042203

394.31

0.2653

0.3470

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-13T04:42:00	Carsten Kossendey	leela	40000	610000		-		-	-	0.022	-	-	1.986%
2012-08-31T05:17:00	Squeeky_Squirrel	P4_2600	90000	1620000		-		-	-	0.055	-	-	2.987%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-10-04T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.219	-	-
2013-11-03T11:16:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.269	-	-
2013-11-19T22:34:00	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	0.512	-	-
2015-06-16T01:50:00	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.025	-	-
2016-10-19T17:39:58	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.050	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.658 GHz-days
Estimated T-Level:	0.250

Digits	B1	Curves	Complete	FacMiss
20	11000	5 / 100	0.050	95.099%
25	50000	5 / 280	0.018	98.227%

New Calculation Method

Total ECM effort:	1.658 GHz-days
Estimated T-Level:	0.250

Digits	B1	Complete	FacMiss
20	11000	0.161	85.104%
25	50000	0.015	98.553%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.995
50000	5000000	18628035398037835973393	2	0.663

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-11-17T12:01:00	Donna Noble	opt4820	50000	5000000						3	0.995
2017-12-14T06:30:04	Bruce	Desk7	50000	5000000	18628035398037835973393	73.980	2	2		2	0.663

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2000-05-05T00:00:00	ANONYMOUS	v4_computers	6A21FEA8E215979A	1.590
2002-02-17T00:00:00	ANONYMOUS	v4_computers	6A21FEA8E215979A	1.590

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-02-26T14:24:26

Oliver Kruse

GTX-0

18628035398037835973393

1318FABDE2DBFF__

2019-04-29T11:41:40

kkmrkkblmbrbk

c5.large

18628035398037835973393

1318FABDE2DBFF86

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 = 90000, B2 = 1620000 (P-1 stage 2)

B1 = 90000 (P-1 stage 1)

B1 = 40000, B2 = 610000 (P-1 stage 2)

B1 = 40000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

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