M14724539 Mersenne number exponent details

Residue

Status

L-L

2DF8A269EBD0E314

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	2.0180	64.1791%	180000	4005000	0.2697	4.4737%	2.2877	65.7816%	1.6025%
PrimeNet	2⁶⁵	0.4955	63.0769%	65000	1900000	0.1146	4.0875%	0.6100	64.5862%	1.5092%
GPU72	2⁶⁹	8.1080	65.2174%	100000	2600000	0.1640	2.9851%	8.2720	66.2557%	1.0383%
Difference	-2	-6.0900	-1.0383%	+80000	+1405000	+0.1057	+1.4886%	-5.9844	-0.4741%	-0.4741%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

2.0180

64.1791%

180000

4005000

0.2697

4.4737%

2.2877

65.7816%

1.6025%

PrimeNet

2⁶⁵

0.4955

63.0769%

65000

1900000

0.1146

4.0875%

0.6100

64.5862%

1.5092%

GPU72

2⁶⁹

8.1080

65.2174%

100000

2600000

0.1640

2.9851%

8.2720

66.2557%

1.0383%

Difference

-2

-6.0900

-1.0383%

+80000

+1405000

+0.1057

+1.4886%

-5.9844

-0.4741%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
14724539	6071982909154473029903	22	72.363	206185840831909 181 × 1139148291889	2016-11-03	181	1139148291889	67.325	43,097	80,492

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

14724539

6071982909154473029903

72.363

206185840831909
181 × 1139148291889

2016-11-03

181

1139148291889

67.325

43,097

80,492

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-02-03T00:00:00	ANONYMOUS	v4_computers	180000	4005000		-		-	-	0.270	-	-	4.474%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-08-24T00:00:00	Net_Force	v4_computers	2¹	2⁵⁶		-	-	0.001	-	-
2000-08-31T00:00:00	Net_Force	v4_computers	2¹	2⁵⁷		-	-	0.001	-	-
2000-09-08T00:00:00	Net_Force	v4_computers	2¹	2⁵⁸		-	-	0.003	-	-
2000-09-23T00:00:00	Net_Force	v4_computers	2¹	2⁵⁹		-	-	0.005	-	-
2000-11-25T00:00:00	Team_Deutschland	v4_computers	2¹	2⁶⁵		-	-	0.495	-	-
2014-09-05T07:21:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.508	-	-
2015-10-10T04:21:04	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	1.015	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.728 GHz-days
Estimated T-Level:	0.050

Digits	B1	Curves	Complete	FacMiss
20	11000	1 / 100	0.010	99.000%
25	50000	1 / 280	0.004	99.643%

New Calculation Method

Total ECM effort:	0.728 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.032	96.826%
25	50000	0.003	99.709%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	6071982909154473029903	1	0.728

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-11-03T16:09:04	Bruce	Desk2	50000	5000000	6071982909154473029903	72.363	1	2		1	0.728

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2003-09-21T00:00:00	Architects Cubed	v4_computers	2DF8A269EBD0E314	7.051
2005-12-24T00:00:00	Team Prime Rib	v4_computers	2DF8A269EBD0E314	7.051

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 = 180000, B2 = 4005000 (P-1 stage 2)

B1 = 180000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁵⁹

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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