M2486971 Mersenne number exponent details

Residue

Status

L-L

139F8B63904478FF

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	11.9478	67.1642%	2382500	2382500	0.2396	3.7038%	12.1875	68.3803%	1.2162%
PrimeNet	2⁵⁹	0.0309	62.7119%	10000	180000	0.0019	2.5354%	0.0328	63.6573%	0.9454%
GPU72	2⁶³	0.6418	65.0794%	11000	160000	0.0019	1.3806%	0.6437	65.5615%	0.4821%
Difference	+4	+11.3061	+2.0848%	+2371500	+2222500	+0.2377	+2.3231%	+11.5438	+2.8189%	+2.8189%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

11.9478

67.1642%

2382500

0.2396

3.7038%

12.1875

68.3803%

1.2162%

PrimeNet

2⁵⁹

0.0309

62.7119%

10000

180000

0.0019

2.5354%

0.0328

63.6573%

0.9454%

GPU72

2⁶³

0.6418

65.0794%

11000

160000

0.0019

1.3806%

0.6437

65.5615%

0.4821%

Difference

+11.3061

+2.0848%

+2371500

+2222500

+0.2377

+2.3231%

+11.5438

+2.8189%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2486971	526406741719241710901816239	27	88.766	105832907122608528789 3 × 71 × 307 × 9497 × 230597 × 739031	2014-11-17	230597	739031	32,783,798	0.0260	0.0472

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2486971

526406741719241710901816239

88.766

105832907122608528789
3 × 71 × 307 × 9497 × 230597 × 739031

2014-11-17

230597

739031

32,783,798

0.0260

0.0472

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.290%
2003-10-31T00:00:00	Team Prime Rib	v4_computers	15000	228750		-		-	-	0.003	-	-	0.919%
2010-12-22T11:37:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.314%
2011-01-22T13:27:00	Oscar Östlin		95000	1947500		-		-	-	0.020	-	-	2.680%
2014-09-03T20:52:00	Jocelyn Larouche	Manual testing	120808	120808		-		-	-	0.012	-	-	1.053%
2014-11-17T10:33:00	mikr	MSI	2382500	2382500			526406741719241710901816239	27	88.766	0.240	0.345	0.479	3.704%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.031	-	-
2022-03-10T05:53:01	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.062	-	-
2009-01-11T08:38:00	Sturle Sunde	giny.ifi	2⁶⁰	2⁶¹		-	-	0.062	-	-
2012-06-10T13:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.124	-	-
2013-01-14T11:53:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.395	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.102 GHz-days
Estimated T-Level:	0.600

Digits	B1	Curves	Complete	FacMiss
20	11000	12 / 100	0.120	88.638%
25	50000	12 / 280	0.043	95.797%

New Calculation Method

Total ECM effort:	1.102 GHz-days
Estimated T-Level:	0.600

Digits	B1	Complete	FacMiss
20	11000	0.387	67.903%
25	50000	0.035	96.562%
30	250000	0.002	99.785%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.102

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-14T08:36:00	Aca Arsov	backo6400	50000	5000000						3	0.276
2010-03-28T03:02:00	James Classen	towerofart	50000	5000000						3	0.276
2012-06-15T00:34:00	Jacques MOLNE	Crazy_64	50000	5000000						3	0.276
2014-02-09T10:46:00	Andy Incline	Office-PC	50000	5000000						3	0.276

date	userid	compid	res64	spent (GHz-days)
1999-05-16T00:00:00	ANONYMOUS	v4_computers	139F8B63904478FF	0.172

date

userid

compid

res64

spent (GHz-days)

1999-05-16T00:00:00

ANONYMOUS

v4_computers

139F8B63904478FF

0.172

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-14T06:26:08

Oliver Kruse

GTX-0

7B52E17E522AC0__

2017-11-29T20:03:31

ATH

ec2-1xf

526406741719241710901816239

7B52E17E522AC0__

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 = 2382500 (P-1 stage 1)

B1 = 95000, B2 = 1947500 (P-1 stage 2)

B1 = 120808 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

B1 = 15000, B2 = 228750 (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)

10²

10³

10⁴

10⁵

10⁶

10⁷

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