M2484721 Mersenne number exponent details

Residue

Status

L-L

DCF83121CA91846C

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	11.9587	67.1642%	2382500	85770100	0.6965	8.1971%	12.6552	69.8558%	2.6916%
PrimeNet	2⁵⁹	0.0309	62.7119%	10000	180000	0.0019	2.5350%	0.0328	63.6571%	0.9452%
GPU72	2⁶³	0.6423	65.0794%	11000	160000	0.0019	1.3804%	0.6443	65.5614%	0.4820%
Difference	+4	+11.3163	+2.0848%	+2371500	+85610100	+0.6946	+6.8167%	+12.0109	+4.2944%	+4.2944%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

11.9587

67.1642%

2382500

85770100

0.6965

8.1971%

12.6552

69.8558%

2.6916%

PrimeNet

2⁵⁹

0.0309

62.7119%

10000

180000

0.0019

2.5350%

0.0328

63.6571%

0.9452%

GPU72

2⁶³

0.6423

65.0794%

11000

160000

0.0019

1.3804%

0.6443

65.5614%

0.4820%

Difference

+11.3163

+2.0848%

+2371500

+85610100

+0.6946

+6.8167%

+12.0109

+4.2944%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2484721	810224964129513803671104679	27	89.388	163041436871486537859 3² × 11 × 67 × 2381 × 389891 × 26478013	2014-11-10	389891	26478013	65,954,613	0.1822	0.2710

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2484721

810224964129513803671104679

89.388

163041436871486537859
3² × 11 × 67 × 2381 × 389891 × 26478013

2014-11-10

389891

26478013

65,954,613

0.1822

0.2710

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	-	-	0.313%
2011-01-21T23:28:00	Oscar Östlin		95000	1947500		-		-	-	0.020	-	-	2.680%
2014-09-03T20:52:00	Jocelyn Larouche	Manual testing	120832	120832		-		-	-	0.012	-	-	1.053%
2014-11-10T17:52:00	mikr	MSI	2382500	85770100	12		810224964129513803671104679	27	89.388	0.697	0.345	1.393	8.197%

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	-	-
2009-01-14T06:51:00	Sturle Sunde	gobi.ifi	2⁶⁰	2⁶¹		-	-	0.062	-	-
2012-06-09T09:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.124	-	-
2013-12-04T21:13:00	Jerry Hallett	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
2009-02-11T07:20:00	maxybo	CB418E216	50000	5000000						3	0.276
2010-03-26T13:37:00	James Classen	towerofart	50000	5000000						3	0.276
2012-06-11T23:10:00	Jacques MOLNE	Crazy_64	50000	5000000						3	0.276
2014-02-07T10:30:00	Andy Incline	Office-PC	50000	5000000						3	0.276

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2000-01-12T00:00:00	ANONYMOUS	v4_computers	DCF83121CA91846C	0.172
2001-03-25T00:00:00	ANONYMOUS	v4_computers	DCF83121CA91846C	0.172

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-14T05:11:25

Oliver Kruse

GTX-2

BB9CDACD225DA1__

2017-11-30T04:45:40

kkmrkkblmbrbk

old

810224964129513803671104679

BB9CDACD225DA1__

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, B2 = 85770100 (P-1 stage 2)

B1 = 2382500 (P-1 stage 1)

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

B1 = 120832 (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

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