M2990381 Mersenne number exponent details

Residue

Status

L-L

0DA10D58C278A4C3

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	9.9365	67.1642%	100000	2025000	0.0253	2.8077%	9.9618	68.0861%	0.9219%
PrimeNet	2⁶⁰	0.0514	63.3333%	12000	220000	0.0029	2.5136%	0.0542	64.2550%	0.9217%
GPU72	2⁶⁴	1.1903	65.6250%	13000	200000	0.0029	1.3860%	1.1931	66.1015%	0.4765%
Difference	+3	+8.7462	+1.5392%	+87000	+1825000	+0.0224	+1.4216%	+8.7687	+1.9847%	+1.9847%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

9.9365

67.1642%

100000

2025000

0.0253

2.8077%

9.9618

68.0861%

0.9219%

PrimeNet

2⁶⁰

0.0514

63.3333%

12000

220000

0.0029

2.5136%

0.0542

64.2550%

0.9217%

GPU72

2⁶⁴

1.1903

65.6250%

13000

200000

0.0029

1.3860%

1.1931

66.1015%

0.4765%

Difference

+8.7462

+1.5392%

+87000

+1825000

+0.0224

+1.4216%

+8.7687

+1.9847%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2990381	4478442278244609002776351	25	81.889	748807974342501675 3 × 5² × 7 × 1426300903509527	2016-01-13	25	1426300903509527	264,265	9,590,130	17,911,693

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2990381

4478442278244609002776351

81.889

748807974342501675
3 × 5² × 7 × 1426300903509527

2016-01-13

1426300903509527

264,265

9,590,130

17,911,693

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%
2010-10-22T13:28:00	markr	tiny	100000	2025000		-		-	-	0.025	-	-	2.808%

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		-	-	0.051	-	-
1999-09-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.051	-	-
2009-02-14T04:36:00	Sturle Sunde	othello.ifi	2⁶⁰	2⁶¹		-	-	0.051	-	-
2011-11-24T05:17:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.103	-	-
2013-01-07T13:51:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.328	-	-
2015-02-05T07:22:00	lycorn	Manual testing	2⁶³	2⁶⁴		-	-	0.657	-	-
2015-02-05T07:23:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	1.249	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.393 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:	1.393 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		9	1.045
50000	5000000	4478442278244609002776351	3	0.348

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-16T16:08:00	James Heinrich	Q6600	50000	5000000						3	0.348
2011-05-10T23:13:00	hentorboeh	FX-6100_Six-Core	50000	5000000						3	0.348
2013-08-07T08:22:00	Richard Kint	xps	50000	5000000						3	0.348
2016-01-13T09:16:21	Bruce	Desk7	50000	5000000	4478442278244609002776351	81.889	3	2		3	0.348

date	userid	compid	res64	spent (GHz-days)
1999-11-10T00:00:00	ANONYMOUS	v4_computers	0DA10D58C278A4C3	0.255

date

userid

compid

res64

spent (GHz-days)

1999-11-10T00:00:00

ANONYMOUS

v4_computers

0DA10D58C278A4C3

0.255

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:33:10

alpertron

Manual testing

4478442278244609002776351

CA114C4BF20E5A__

2017-11-18T04:24:33

Oliver Kruse

GTX-2

4478442278244609002776351

CA114C4BF20E5A__

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 = 100000, B2 = 2025000 (P-1 stage 2)

B1 = 100000 (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