M2783923 Mersenne number exponent details

Residue

Status

L-L

0ECC43AF2074D31C

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	10.6734	67.1642%	100000	2075000	0.0233	2.7936%	10.6966	68.0815%	0.9173%
PrimeNet	2⁵⁹	0.0276	62.7119%	12000	220000	0.0026	2.8588%	0.0302	63.7779%	1.0660%
GPU72	2⁶³	0.5733	65.0794%	15000	240000	0.0031	1.7479%	0.5764	65.6898%	0.6104%
Difference	+4	+10.1001	+2.0848%	+85000	+1835000	+0.0202	+1.0457%	+10.1203	+2.3917%	+2.3917%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

10.6734

67.1642%

100000

2075000

0.0233

2.7936%

10.6966

68.0815%

0.9173%

PrimeNet

2⁵⁹

0.0276

62.7119%

12000

220000

0.0026

2.8588%

0.0302

63.7779%

1.0660%

GPU72

2⁶³

0.5733

65.0794%

15000

240000

0.0031

1.7479%

0.5764

65.6898%

0.6104%

Difference

+10.1001

+2.0848%

+85000

+1835000

+0.0202

+1.0457%

+10.1203

+2.3917%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2783923	14044242768402761249873	23	73.572	2522383479787832 2³ × 1027421 × 306882899	2015-03-17	1027421	306882899	1,048.8	1.9813	3.4973

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2783923

14044242768402761249873

73.572

2522383479787832
2³ × 1027421 × 306882899

2015-03-17

1027421

306882899

1,048.8

1.9813

3.4973

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-17T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.300%
2010-11-11T04:19:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.002	-	-	0.253%
2010-11-25T17:51:00	markr	tiny	100000	2075000		-		-	-	0.023	-	-	2.794%
2014-10-28T23:25:00	Jocelyn Larouche	Manual testing	123055	123055		-		-	-	0.014	-	-	1.086%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-01-28T15:29:00	Sturle Sunde	gimba.ifi	2⁶⁰	2⁶¹		-	-	0.055	-	-
2012-04-03T06:33:00	Grant McCracken	home	2⁶¹	2⁶²		-	-	0.110	-	-
2013-01-14T12:31:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.353	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.041 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:	1.041 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	0.937
50000	5000000	14044242768402761249873	1	0.104

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-04T11:19:00	Stun	Core2	50000	5000000						3	0.312
2010-09-27T18:42:00	wallu		50000	5000000						3	0.312
2013-03-12T11:27:00	KAMCOBILL	PC20	50000	5000000						3	0.312
2015-03-17T22:51:00	Bruce	desk16	50000	5000000	14044242768402761249873	73.572	1	2		1	0.104

date	userid	compid	res64	spent (GHz-days)
1999-07-12T00:00:00	Vassilo	v4_computers	0ECC43AF2074D31C	0.215

date

userid

compid

res64

spent (GHz-days)

1999-07-12T00:00:00

Vassilo

v4_computers

0ECC43AF2074D31C

0.215

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-21T07:16:07

Oliver Kruse

GTX-0

14044242768402761249873

4136CCB66B3425__

2017-12-06T08:55:20

kkmrkkblmbrbk

c4.xlarge

14044242768402761249873

4136CCB66B3425__

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 = 2075000 (P-1 stage 2)

B1 = 123055 (P-1 stage 1)

B1 = 100000 (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

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