M2738017 Mersenne number exponent details

Residue

Status

L-L

287A07663C1C6911

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	10.8523	67.1642%	185000	4625000	0.0478	3.6932%	10.9002	68.3769%	1.2127%
PrimeNet	2⁵⁹	0.0280	62.7119%	12000	220000	0.0026	2.8502%	0.0307	63.7747%	1.0628%
GPU72	2⁶³	0.5829	65.0794%	14000	240000	0.0029	1.7076%	0.5859	65.6757%	0.5963%
Difference	+4	+10.2694	+2.0848%	+171000	+4385000	+0.0449	+1.9856%	+10.3143	+2.7012%	+2.7012%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

10.8523

67.1642%

185000

4625000

0.0478

3.6932%

10.9002

68.3769%

1.2127%

PrimeNet

2⁵⁹

0.0280

62.7119%

12000

220000

0.0026

2.8502%

0.0307

63.7747%

1.0628%

GPU72

2⁶³

0.5829

65.0794%

14000

240000

0.0029

1.7076%

0.5859

65.6757%

0.5963%

Difference

+10.2694

+2.0848%

+171000

+4385000

+0.0449

+1.9856%

+10.3143

+2.7012%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2738017	13935499816338843206111	23	73.561	2544816160078415 5 × 71 × 7168496225573	2013-02-22	71	7168496225573	1,384.5	43,740	81,694

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2738017

13935499816338843206111

73.561

2544816160078415
5 × 71 × 7168496225573

2013-02-22

7168496225573

1,384.5

43,740

81,694

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.299%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	225000		-		-	-	0.003	-	-	0.933%
2010-12-19T21:43:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.321%
2010-12-29T20:12:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.439%
2011-01-20T22:46:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.629%
2011-04-27T07:10:00	James Heinrich	WHS	185000	4625000		-		-	-	0.048	-	-	3.693%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-01-28T04:32:00	Sturle Sunde	papageno.ifi	2⁶⁰	2⁶¹		-	-	0.056	-	-
2012-04-09T19:54:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.112	-	-
2013-01-14T12:27:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.359	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.623 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:	0.623 GHz-days
Estimated T-Level:	0.300

Digits	B1	Complete	FacMiss
20	11000	0.231	79.392%
25	50000	0.021	97.887%
30	250000	0.001	99.865%

ECM Summary

B1	B2	factor	curves	GHz-days
		13935499816338843206111	1	0.00000e+0
50000	5000000		6	0.623

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-16T19:01:00	Lukasz Wrobel	UNIX_05	50000	5000000						3	0.311
2010-09-01T01:19:00	James Classen	towerofart	50000	5000000						3	0.311
2013-02-22T17:58:00	jim f in mn	asus			13935499816338843206111	73.561		1		1	-

date	userid	compid	res64	spent (GHz-days)
1999-07-12T00:00:00	ANONYMOUS	v4_computers	287A07663C1C6911	0.211

date

userid

compid

res64

spent (GHz-days)

1999-07-12T00:00:00

ANONYMOUS

v4_computers

287A07663C1C6911

0.211

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-20T06:41:00

Oliver Kruse

GTX-3

13935499816338843206111

868ECAA8FC0970__

2017-12-05T11:33:19

kkmrkkblmbrbk

c4.xlarge

13935499816338843206111

868ECAA8FC0970__

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 = 185000, B2 = 4625000 (P-1 stage 2)

B1 = 185000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 225000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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