M4869167 Mersenne number exponent details

Residue

Status

L-L

A77EFD6421EFE79C

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	6.1025	65.6716%	410000	11070000	0.1991	5.2646%	6.3016	67.4789%	1.8072%
PrimeNet	2⁶¹	0.0631	62.2951%	22000	450000	0.0091	3.2987%	0.0722	63.5388%	1.2438%
GPU72	2⁶⁵	1.4983	64.6154%	32000	700000	0.0137	2.3715%	1.5121	65.4545%	0.8391%
Difference	+2	+4.6041	+1.0563%	+378000	+10370000	+0.1854	+2.8931%	+4.7895	+2.0244%	+2.0244%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.1025

65.6716%

410000

11070000

0.1991

5.2646%

6.3016

67.4789%

1.8072%

PrimeNet

2⁶¹

0.0631

62.2951%

22000

450000

0.0091

3.2987%

0.0722

63.5388%

1.2438%

GPU72

2⁶⁵

1.4983

64.6154%

32000

700000

0.0137

2.3715%

1.5121

65.4545%

0.8391%

Difference

+4.6041

+1.0563%

+378000

+10370000

+0.1854

+2.8931%

+4.7895

+2.0244%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4869167	269161363790609284121	21	67.867	27639364576180 2² × 5 × 7² × 1579 × 17861579	2017-04-15	1579	17861579	6.4745	0.1959	0.3653

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4869167

269161363790609284121

67.867

27639364576180
2² × 5 × 7² × 1579 × 17861579

2017-04-15

1579

17861579

6.4745

0.1959

0.3653

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-16T19:46:00	Carsten Kossendey	durandal	30000	435000		-		-	-	0.010	-	-	1.570%
2013-12-20T13:26:00	David Campeau	i5-2500k	410000	11070000		-		-	-	0.199	-	-	5.265%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:39:03	Mark Rose	Manual testing	2¹	2⁶¹		-	-	0.063	-	-
2010-04-23T00:43:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.063	-	-
2011-10-09T22:43:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.328	-	-
2016-02-23T16:39:03	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.202	-	-
2015-01-09T11:16:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.403	-	-
2015-01-09T11:16:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.767	-	-
2015-07-21T21:29:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.535	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.675 GHz-days
Estimated T-Level:	0.400

Digits	B1	Curves	Complete	FacMiss
20	11000	8 / 100	0.080	92.274%
25	50000	8 / 280	0.029	97.178%

New Calculation Method

Total ECM effort:	1.675 GHz-days
Estimated T-Level:	0.400

Digits	B1	Complete	FacMiss
20	11000	0.308	73.514%
25	50000	0.028	97.193%
30	250000	0.002	99.821%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	1.256
50000	5000000	269161363790609284121	2	0.419

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-04-04T08:42:00	zampel	maloja	50000	5000000						3	0.628
2014-02-13T22:44:00	S36049	Wolle6	50000	5000000						3	0.628
2017-04-15T21:48:54	Bruce	desk	50000	5000000	269161363790609284121	67.867	2	2		2	0.419

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-06-01T00:00:00	Kimon Berlin	v4_computers	A77EFD6421EFE79C	0.675
2000-03-22T00:00:00	Stephan Grupp	v4_computers	A77EFD6421EFE79C	0.675

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-20T10:27:19

kkmrkkblmbrbk

c4.xlarge

269161363790609284121

28C7D6D9B23225__

2018-04-01T15:42:52

Oliver Kruse

GTX-6

269161363790609284121

28C7D6D9B23225__

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 = 410000, B2 = 11070000 (P-1 stage 2)

B1 = 410000 (P-1 stage 1)

B1 = 30000, B2 = 435000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

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