M6902219 Mersenne number exponent details

Residue

Status

L-L

54ED019D7D00F7D2

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	4.3050	65.6716%	130000	2665000	0.0848	3.5282%	4.3898	66.8828%	1.2112%
PrimeNet	2⁶³	0.2312	63.4921%	28000	700000	0.0204	3.1587%	0.2517	64.6452%	1.1532%
GPU72	2⁶⁷	4.3050	65.6716%	45000	900000	0.0290	2.2353%	4.3339	66.4390%	0.7674%
Difference	-	-	-	+85000	+1765000	+0.0558	+1.2929%	+0.0558	+0.4438%	+0.4438%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

4.3050

65.6716%

130000

2665000

0.0848

3.5282%

4.3898

66.8828%

1.2112%

PrimeNet

2⁶³

0.2312

63.4921%

28000

700000

0.0204

3.1587%

0.2517

64.6452%

1.1532%

GPU72

2⁶⁷

4.3050

65.6716%

45000

900000

0.0290

2.2353%

4.3339

66.4390%

0.7674%

Difference

+85000

+1765000

+0.0558

+1.2929%

+0.0558

+0.4438%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6902219	30702279275172579785281	23	74.701	2224087592350560 2⁵ × 3 × 5 × 691 × 2347 × 2857061	2017-03-29	2347	2857061	842.25	0.0499	0.0919

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

6902219

30702279275172579785281

74.701

2224087592350560
2⁵ × 3 × 5 × 691 × 2347 × 2857061

2017-03-29

2347

2857061

842.25

0.0499

0.0919

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-08-24T00:00:00	lettp	v4_computers	30000	270000		-		-	-	0.014	-	-	1.452%
2011-11-19T09:18:00	James Heinrich	i7-920	130000	2665000		-		-	-	0.085	-	-	3.528%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-05T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.089	-	-
2005-01-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.231	-	-
2014-02-09T10:09:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.284	-	-
2014-02-17T23:33:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.541	-	-
2015-06-21T19:55:00	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.083	-	-
2016-03-31T14:38:48	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.165	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.326 GHz-days
Estimated T-Level:	0.200

Digits	B1	Curves	Complete	FacMiss
20	11000	4 / 100	0.040	96.060%
25	50000	4 / 280	0.014	98.579%

New Calculation Method

Total ECM effort:	1.326 GHz-days
Estimated T-Level:	0.200

Digits	B1	Complete	FacMiss
20	11000	0.129	87.895%
25	50000	0.012	98.841%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.995
50000	5000000	30702279275172579785281	1	0.332

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-08-11T02:37:00	vichico	HP-ROMA	50000	5000000						3	0.995
2017-03-29T14:16:40	Bruce	Desk8	50000	5000000	30702279275172579785281	74.701	1	2		1	0.332

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-07-27T00:00:00	ANONYMOUS	v4_computers	54ED019D7D00F7D2	1.505
2001-10-13T00:00:00	lettp	v4_computers	54ED019D7D00F7D2	1.505

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-01-21T02:21:04

Oliver Kruse

GTX-0

30702279275172579785281

13BA145A103A0B__

2019-01-22T22:02:14

Zero

DELL380

30702279275172579785281

13BA145A103A0B5B

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 = 130000, B2 = 2665000 (P-1 stage 2)

B1 = 130000 (P-1 stage 1)

B1 = 30000, B2 = 270000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

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