M6902759 Mersenne number exponent details

Residue

Status

L-L

278F01AE24A3F3B0

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	4.3046	65.6716%	130000	2665000	0.0848	3.5282%	4.3894	66.8828%	1.2112%
PrimeNet	2⁶³	0.2312	63.4921%	28000	700000	0.0204	3.1587%	0.2516	64.6453%	1.1532%
GPU72	2⁶⁷	4.3046	65.6716%	45000	900000	0.0290	2.2354%	4.3336	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

4.3046

65.6716%

130000

2665000

0.0848

3.5282%

4.3894

66.8828%

1.2112%

PrimeNet

2⁶³

0.2312

63.4921%

28000

700000

0.0204

3.1587%

0.2516

64.6453%

1.1532%

GPU72

2⁶⁷

4.3046

65.6716%

45000

900000

0.0290

2.2354%

4.3336

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
6902759	10789413221159920543433	23	73.192	781529039414524 2² × 3818641 × 51165391	2017-03-24	3818641	51165391	388.93	2.0230	2.4572

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

6902759

10789413221159920543433

73.192

781529039414524
2² × 3818641 × 51165391

2017-03-24

3818641

51165391

388.93

2.0230

2.4572

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-11-24T00:00:00	AZMango	v4_computers	35000	341250		-		-	-	0.016	-	-	1.618%
2011-11-19T14:29:00	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
1998-06-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.045	-	-
1998-07-05T00:00:00	slaur	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	-	-
2016-03-31T14:38:49	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.165	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.989 GHz-days
Estimated T-Level:	0.300

Digits	B1	Curves	Complete	FacMiss
20	11000	6 / 100	0.060	94.148%
25	50000	6 / 280	0.021	97.876%

New Calculation Method

Total ECM effort:	1.989 GHz-days
Estimated T-Level:	0.300

Digits	B1	Complete	FacMiss
20	11000	0.194	82.403%
25	50000	0.017	98.266%
30	250000	0.001	99.892%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.995
50000	5000000	10789413221159920543433	3	0.995

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-08-18T09:34:00	vichico	NEO1	50000	5000000						3	0.995
2017-03-24T18:51:57	Bruce	Desk7	50000	5000000	10789413221159920543433	73.192	3	2		3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-02T00:00:00	ANONYMOUS	v4_computers	278F01AE24A3F3B0	1.505
2001-12-22T00:00:00	AZMango	v4_computers	278F01AE24A3F3B0	1.505

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-01-21T23:01:43

Oliver Kruse

GTX-3

10789413221159920543433

E3D167B311CEB3__

2019-01-22T12:42:16

kracker

GRID-11

10789413221159920543433

E3D167B311CEB365

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 = 35000, B2 = 341250 (P-1 stage 2)

B1 = 35000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

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