M2111093 Mersenne number exponent details

Residue

Status

L-L

B260CACD692EFD26

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	14.0751	67.1642%	140000	3010000	0.0283	3.1008%	14.1034	68.1823%	1.0182%
PrimeNet	2⁵⁸	0.0182	62.0690%	9000	160000	0.0016	2.6804%	0.0198	63.0857%	1.0167%
GPU72	2⁶²	0.2910	64.5161%	10000	140000	0.0016	1.4529%	0.2926	65.0317%	0.5155%
Difference	+5	+13.7841	+2.6481%	+130000	+2870000	+0.0266	+1.6479%	+13.8107	+3.1507%	+3.1507%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.0751

67.1642%

140000

3010000

0.0283

3.1008%

14.1034

68.1823%

1.0182%

PrimeNet

2⁵⁸

0.0182

62.0690%

9000

160000

0.0016

2.6804%

0.0198

63.0857%

1.0167%

GPU72

2⁶²

0.2910

64.5161%

10000

140000

0.0016

1.4529%

0.2926

65.0317%

0.5155%

Difference

+13.7841

+2.6481%

+130000

+2870000

+0.0266

+1.6479%

+13.8107

+3.1507%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2111093	14397110993287550961431	23	73.608	3409871330464255 5 × 47 × 14510090767933	2016-05-29	47	14510090767933	1,246.4	75,369	140,768

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2111093

14397110993287550961431

73.608

3409871330464255
5 × 47 × 14510090767933

2016-05-29

14510090767933

1,246.4

75,369

140,768

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.277%
2009-08-02T07:55:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	1.021%
2010-12-30T22:20:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.415%
2011-01-10T23:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.596%
2011-01-27T18:15:00	James Heinrich	Q6600	140000	3010000		-		-	-	0.028	-	-	3.101%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-17T00:00:00	Martijn Otto	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:05	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.055	-	-
2009-01-03T09:38:00	Sturle Sunde	ghibu.ifi	2⁶⁰	2⁶¹		-	-	0.073	-	-
2012-03-31T07:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.146	-	-
2013-09-05T08:28:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.465	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.930	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.770	-	-
2015-12-27T16:49:19	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.540	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.959 GHz-days
Estimated T-Level:	1.150

Digits	B1	Curves	Complete	FacMiss
20	11000	23 / 100	0.230	79.361%
25	50000	23 / 280	0.082	92.100%

New Calculation Method

Total ECM effort:	1.959 GHz-days
Estimated T-Level:	1.150

Digits	B1	Complete	FacMiss
20	11000	0.742	47.619%
25	50000	0.067	93.514%
30	250000	0.004	99.588%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		21	1.788
50000	5000000	14397110993287550961431	2	0.170

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-13T10:03:00	borkencode	CFF2DC1CD	50000	5000000						3	0.255
2009-11-10T18:33:00	Samoflan	Parker	50000	5000000						3	0.255
2011-07-06T11:45:00	Lukasz Wrobel	w-s	50000	5000000						3	0.255
2013-04-10T09:50:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.255
2014-11-04T04:08:00	arnaud	srv-630	50000	5000000						3	0.255
2015-08-04T00:19:00	guru	w1	50000	5000000						3	0.255
2016-02-24T15:23:50	Hartmut Birr	C7CE7B89E	50000	5000000						3	0.255
2016-05-29T18:43:03	Bruce	Desk6	50000	5000000	14397110993287550961431	73.608	2	2		2	0.170

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	Martijn Otto	v4_computers	B260CACD692EFD26	0.139

date

userid

compid

res64

spent (GHz-days)

1999-01-29T00:00:00

Martijn Otto

v4_computers

B260CACD692EFD26

0.139

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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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