M2561981 Mersenne number exponent details

Residue

Status

L-L

EAF7D46D4EF949FE

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	11.5980	67.1642%	175000	4068750	0.0389	3.5307%	11.6370	68.3235%	1.1593%
PrimeNet	2⁵⁹	0.0300	62.7119%	11000	200000	0.0021	2.6876%	0.0321	63.7140%	1.0021%
GPU72	2⁶³	0.6230	65.0794%	12000	180000	0.0021	1.4794%	0.6251	65.5960%	0.5166%
Difference	+4	+10.9751	+2.0848%	+163000	+3888750	+0.0368	+2.0513%	+11.0119	+2.7275%	+2.7275%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

11.5980

67.1642%

175000

4068750

0.0389

3.5307%

11.6370

68.3235%

1.1593%

PrimeNet

2⁵⁹

0.0300

62.7119%

11000

200000

0.0021

2.6876%

0.0321

63.7140%

1.0021%

GPU72

2⁶³

0.6230

65.0794%

12000

180000

0.0021

1.4794%

0.6251

65.5960%

0.5166%

Difference

+10.9751

+2.0848%

+163000

+3888750

+0.0368

+2.0513%

+11.0119

+2.7275%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2561981	2427590870899238899369	22	71.040	473772223700964 2² × 3³ × 16231 × 270271693	2015-08-13	16231	270271693	219.09	1.4825	2.7660

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2561981

2427590870899238899369

71.040

473772223700964
2² × 3³ × 16231 × 270271693

2015-08-13

16231

270271693

219.09

1.4825

2.7660

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-23T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.293%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	198750		-		-	-	0.003	-	-	0.885%
2010-12-21T01:09:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.316%
2011-01-03T14:36:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.433%
2011-01-10T23:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.620%
2011-04-12T22:53:00	James Heinrich	WHS	175000	4068750		-		-	-	0.039	-	-	3.531%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2022-03-11T02:05:00	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.060	-	-
2009-01-31T19:13:00	Sturle Sunde	gouffy.ifi	2⁶⁰	2⁶¹		-	-	0.060	-	-
2012-06-17T08:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.120	-	-
2013-01-14T11:55:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.383	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.766	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.458	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.384 GHz-days
Estimated T-Level:	0.750

Digits	B1	Curves	Complete	FacMiss
20	11000	15 / 100	0.150	86.006%
25	50000	15 / 280	0.054	94.775%

New Calculation Method

Total ECM effort:	1.384 GHz-days
Estimated T-Level:	0.750

Digits	B1	Complete	FacMiss
20	11000	0.484	61.639%
25	50000	0.044	95.721%
30	250000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.107
50000	5000000	2427590870899238899369	3	0.277

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-16T12:01:00	S36049	Wolle3	50000	5000000						3	0.277
2010-05-10T14:39:00	James Hintz	ryan	50000	5000000						3	0.277
2012-12-15T07:52:00	Smurgs	Praca	50000	5000000						3	0.277
2014-04-18T06:57:00	Andy Incline	Office-PC	50000	5000000						3	0.277
2015-08-13T03:41:00	guru	w1	50000	5000000	2427590870899238899369	71.040	3	2		3	0.277

date	userid	compid	res64	spent (GHz-days)
1999-04-13T00:00:00	PhillT	v4_computers	EAF7D46D4EF949FE	0.178

date

userid

compid

res64

spent (GHz-days)

1999-04-13T00:00:00

PhillT

v4_computers

EAF7D46D4EF949FE

0.178

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-15T01:56:20

Oliver Kruse

GTX-3

2427590870899238899369

EAB4C9B8538570__

2017-12-01T17:43:50

kkmrkkblmbrbk

c4.xlarge

2427590870899238899369

EAB4C9B8538570__

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 = 175000, B2 = 4068750 (P-1 stage 2)

B1 = 175000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 198750 (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

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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