M2981533 Mersenne number exponent details

Residue

Status

L-L

A430099B3DA46C6D

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	9.9660	67.1642%	95000	1995000	0.0245	2.7701%	9.9905	68.0738%	0.9096%
PrimeNet	2⁶⁰	0.0515	63.3333%	12000	220000	0.0029	2.5122%	0.0544	64.2545%	0.9212%
GPU72	2⁶⁴	1.1938	65.6250%	13000	200000	0.0029	1.3852%	1.1967	66.1012%	0.4762%
Difference	+3	+8.7722	+1.5392%	+82000	+1795000	+0.0216	+1.3848%	+8.7938	+1.9726%	+1.9726%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

9.9660

67.1642%

95000

1995000

0.0245

2.7701%

9.9905

68.0738%

0.9096%

PrimeNet

2⁶⁰

0.0515

63.3333%

12000

220000

0.0029

2.5122%

0.0544

64.2545%

0.9212%

GPU72

2⁶⁴

1.1938

65.6250%

13000

200000

0.0029

1.3852%

1.1967

66.1012%

0.4762%

Difference

+8.7722

+1.5392%

+82000

+1795000

+0.0216

+1.3848%

+8.7938

+1.9726%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2981533	50178704961948907856999	23	75.409	8414916917228303 8414916917228303	2016-01-10	1	8414916917228303	4,245.8	56,580,031	105,675,742

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2981533

50178704961948907856999

75.409

8414916917228303
8414916917228303

2016-01-10

8414916917228303

4,245.8

56,580,031

105,675,742

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-13T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.306%
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.177%
2010-10-25T09:59:00	markr	tiny	95000	1995000		-		-	-	0.024	-	-	2.770%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.052	-	-
2009-02-13T05:44:00	Sturle Sunde	gorilla.ifi	2⁶⁰	2⁶¹		-	-	0.052	-	-
2011-11-25T23:12:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.103	-	-
2013-01-07T13:51:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.329	-	-
2015-04-13T19:44:00	lycorn	Manual testing	2⁶³	2⁶⁴		-	-	0.658	-	-
2015-04-13T19:44:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	1.253	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.160 GHz-days
Estimated T-Level:	0.500

Digits	B1	Curves	Complete	FacMiss
20	11000	10 / 100	0.100	90.438%
25	50000	10 / 280	0.036	96.485%

New Calculation Method

Total ECM effort:	1.160 GHz-days
Estimated T-Level:	0.500

Digits	B1	Complete	FacMiss
20	11000	0.323	72.428%
25	50000	0.029	97.127%
30	250000	0.002	99.821%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.044
50000	5000000	50178704961948907856999	1	0.116

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-13T10:38:00	James Heinrich	Q6600	50000	5000000						3	0.348
2011-05-08T19:02:00	sannerud.com	Jens2010	50000	5000000						3	0.348
2013-07-31T18:45:00	Youcef L	breitner	50000	5000000						3	0.348
2016-01-10T22:50:23	Bruce	Desk7	50000	5000000	50178704961948907856999	75.409	1	2		1	0.116

date	userid	compid	res64	spent (GHz-days)
1999-08-16T00:00:00	ANONYMOUS	v4_computers	A430099B3DA46C6D	0.254

date

userid

compid

res64

spent (GHz-days)

1999-08-16T00:00:00

ANONYMOUS

v4_computers

A430099B3DA46C6D

0.254

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:33:05

alpertron

Manual testing

50178704961948907856999

9C04AF7DC1B0A7__

2017-11-18T03:11:19

Oliver Kruse

GTX-2

50178704961948907856999

9C04AF7DC1B0A7__

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 = 95000, B2 = 1995000 (P-1 stage 2)

B1 = 95000 (P-1 stage 1)

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

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

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