M2119463 Mersenne number exponent details

Residue

Status

L-L

332BAC2D904C19BE

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	14.0196	67.1642%	140000	3010000	0.0283	3.1025%	14.0478	68.1829%	1.0187%
PrimeNet	2⁵⁸	0.0181	62.0690%	9000	160000	0.0016	2.6824%	0.0198	63.0864%	1.0175%
GPU72	2⁶²	0.2899	64.5161%	10000	140000	0.0016	1.4540%	0.2915	65.0321%	0.5159%
Difference	+5	+13.7297	+2.6481%	+130000	+2870000	+0.0266	+1.6485%	+13.7563	+3.1508%	+3.1508%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.0196

67.1642%

140000

3010000

0.0283

3.1025%

14.0478

68.1829%

1.0187%

PrimeNet

2⁵⁸

0.0181

62.0690%

9000

160000

0.0016

2.6824%

0.0198

63.0864%

1.0175%

GPU72

2⁶²

0.2899

64.5161%

10000

140000

0.0016

1.4540%

0.2915

65.0321%

0.5159%

Difference

+13.7297

+2.6481%

+130000

+2870000

+0.0266

+1.6485%

+13.7563

+3.1508%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2119463	96266763216595369622743	23	76.349	22710177817823517 3 × 7 × 1217 × 888608906281	2016-06-03	1217	888608906281	13,030	4,615.7	8,620.8

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2119463

96266763216595369622743

76.349

22710177817823517
3 × 7 × 1217 × 888608906281

2016-06-03

1217

888608906281

13,030

4,615.7

8,620.8

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-07-21T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.277%
2009-08-02T19:43:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	1.022%
2010-12-30T22:21:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.416%
2011-01-11T22:55:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.597%
2011-01-25T14:46:00	James Heinrich	i7-920	140000	3010000		-		-	-	0.028	-	-	3.103%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:05	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.054	-	-
2009-01-03T07:01:00	Sturle Sunde	giovanni.ifi	2⁶⁰	2⁶¹		-	-	0.072	-	-
2012-04-02T05:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.145	-	-
2013-09-06T08:31:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.463	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.926	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.763	-	-
2016-01-06T22:34:25	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.526	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.045 GHz-days
Estimated T-Level:	1.200

Digits	B1	Curves	Complete	FacMiss
20	11000	24 / 100	0.240	78.568%
25	50000	24 / 280	0.086	91.772%

New Calculation Method

Total ECM effort:	2.045 GHz-days
Estimated T-Level:	1.200

Digits	B1	Complete	FacMiss
20	11000	0.774	46.108%
25	50000	0.070	93.242%
30	250000	0.004	99.570%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		21	1.789
50000	5000000	96266763216595369622743	3	0.256

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-23T16:35:00	Battlemaxx	Maxx_mom	50000	5000000						3	0.256
2009-12-02T13:44:00	Vadim Mihailov	motorolla	50000	5000000						3	0.256
2011-07-13T13:57:00	S36049	Wolle5	50000	5000000						3	0.256
2013-04-15T01:23:00	Xyzzy	J	50000	5000000						3	0.256
2014-12-02T16:16:00	arnaud	srv-630	50000	5000000						3	0.256
2015-08-06T22:01:00	guru	w6	50000	5000000						3	0.256
2016-02-23T15:19:38	Bruce	Desk6	50000	5000000						3	0.256
2016-06-03T13:09:53	Bruce	Desk6	50000	5000000	96266763216595369622743	76.349	3	2		3	0.256

date	userid	compid	res64	spent (GHz-days)
1999-02-07T00:00:00	ANONYMOUS	v4_computers	332BAC2D904C19BE	0.139

date

userid

compid

res64

spent (GHz-days)

1999-02-07T00:00:00

ANONYMOUS

v4_computers

332BAC2D904C19BE

0.139

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-07T15:11:53

kkmrkkblmbrbk

c4.xlarge

96266763216595369622743

2629FA15036713__

2017-10-21T15:04:48

Oliver Kruse

GTX-1

96266763216595369622743

2629FA15036713__

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 = 140000, B2 = 3010000 (P-1 stage 2)

B1 = 140000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 260000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 20000 (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

10¹⁰

10¹¹

10¹²

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