M2131691 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	13.9391	67.1642%	500000	15000000	0.1230	5.1625%	14.0621	68.8593%	1.6951%
PrimeNet	2⁵⁸	0.0180	62.0690%	9000	170000	0.0017	2.7294%	0.0197	63.1042%	1.0353%
GPU72	2⁶²	0.2882	64.5161%	10000	150000	0.0017	1.4864%	0.2899	65.0435%	0.5274%
Difference	+5	+13.6509	+2.6481%	+490000	+14850000	+0.1213	+3.6761%	+13.7722	+3.8158%	+3.8158%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.9391

67.1642%

500000

15000000

0.1230

5.1625%

14.0621

68.8593%

1.6951%

PrimeNet

2⁵⁸

0.0180

62.0690%

9000

170000

0.0017

2.7294%

0.0197

63.1042%

1.0353%

GPU72

2⁶²

0.2882

64.5161%

10000

150000

0.0017

1.4864%

0.2899

65.0435%

0.5274%

Difference

+13.6509

+2.6481%

+490000

+14850000

+0.1213

+3.6761%

+13.7722

+3.8158%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2131691	1207338621817	13	40.135	283188 2² × 3 × 23599	-	4	23599	8.906e-8	0.0001	0.0002
2131691	14510538701500017420007	23	73.620	3403527692686233 3 × 7 × 162072747270773	2022-01-02	7	162072747270773	1,113.5	841,846	1,572,335

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2131691

1207338621817

40.135

283188
2² × 3 × 23599

23599

8.906e-8

0.0001

0.0002

2131691

14510538701500017420007

73.620

3403527692686233
3 × 7 × 162072747270773

2022-01-02

162072747270773

1,113.5

841,846

1,572,335

exponent	prime factors	composite factor	digits	bits*
2131691	1207338621817 14510538701500017420007	17519133797691271782472743422492719	35	113.754

exponent

prime factors

composite factor

digits

bits*

2131691

1207338621817
14510538701500017420007

17519133797691271782472743422492719

113.754

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-20T14:55:30	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 1207338621817	-	-	0.123	-	-	5.162%

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.450 GHz-days
Estimated T-Level:	0.800

Digits	B1	Curves	Complete	FacMiss
20	11000	16 / 100	0.160	85.146%
25	50000	16 / 280	0.057	94.436%

New Calculation Method

Total ECM effort:	1.450 GHz-days
Estimated T-Level:	0.800

Digits	B1	Complete	FacMiss
20	11000	0.532	58.760%
25	50000	0.048	95.276%
30	250000	0.003	99.702%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	0.512
50000	5000000	14510538701500017420007	3	0.256
50000	6750000		7	0.682

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-08T09:03:23	ATH	ec2-1xd	50000	5000000						3	0.256
2019-10-16T07:17:00	ATH	ec2-ECMCF	50000	5000000						3	0.256
2022-01-02T23:25:34	MarkS	desktop-i7	50000	5000000	14510538701500017420007	73.620	3	2	3105293693753013	3	0.256
2022-03-05T08:13:38	Dylan Delgado	colab	50000	6750000						7	0.682

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-08T14:50:33

Oliver Kruse

GTX-3

1207338621817

09D8BAECFD276D__

2017-11-18T01:52:57

kkmrkkblmbrbk

c4.xlarge

1207338621817

09D8BAECFD276D__

2022-01-03T07:14:38

MarkS

desktop-i7

1207338621817

14510538701500017420007

A69F38982DD256EE

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (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

10¹⁵

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