M31387 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	946.6951	77.6119%	200000000	5000000000	0.3686	12.3633%	947.0637	80.3798%	2.7679%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	4.1510%	0.0000	64.0566%	1.5566%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.7821%	0.0001	66.5166%	0.6075%
Difference	+23	+946.6950	+11.7028%	+199999500	+4999990000	+0.3686	+10.5812%	+947.0636	+13.8632%	+13.8632%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

946.6951

77.6119%

200000000

5000000000

0.3686

12.3633%

947.0637

80.3798%

2.7679%

PrimeNet

2⁴⁰

0.0000

62.5000%

500

10000

0.0000

4.1510%

0.0000

64.0566%

1.5566%

GPU72

2⁴⁴

0.0001

65.9091%

500

10000

0.0000

1.7821%

0.0001

66.5166%

0.6075%

Difference

+23

+946.6950

+11.7028%

+199999500

+4999990000

+0.3686

+10.5812%

+947.0636

+13.8632%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
31387	59509753	8	25.827	948 2² × 3 × 79	-	4	79	1.716e-10	6.459e-9	6.502e-9
31387	1206346099687	13	40.134	19217289 3 × 7 × 13 × 70393	2008-08-26	13	70393	7.403e-6	3.073e-6	5.721e-6
31387	677255057696161993076824730156639	33	109.061	10788782898909771451187191037 13² × 14897 × 4285356250557485443909	2017-06-11	14897	4285356250557485443909	5.160e+12	1.865e+11	3.483e+11

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

31387

59509753

25.827

948
2² × 3 × 79

1.716e-10

6.459e-9

6.502e-9

31387

1206346099687

40.134

19217289
3 × 7 × 13 × 70393

2008-08-26

70393

7.403e-6

3.073e-6

5.721e-6

31387

677255057696161993076824730156639

109.061

10788782898909771451187191037
13² × 14897 × 4285356250557485443909

2017-06-11

14897

4285356250557485443909

5.160e+12

1.865e+11

3.483e+11

exponent	prime factors	composite factor	digits	bits*
31387	59509753 1206346099687	71789358424886747311	20	65.960
31387	59509753 677255057696161993076824730156639	40303281201499349255989549715913238200167	41	134.888
31387	1206346099687 677255057696161993076824730156639	817003997345059172257555809774967706218871993	45	149.195
31387	59509753 1206346099687 677255057696161993076824730156639	48619706082017127111431598623423313780061636242047 729	53	175.022

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-10-09T01:59:41	kkmrkkblmbrbk	Manual testing	200000000	5000000000	12	-	skipped known factor: 59509753 skipped known factor: 1206346099687	-	-	0.369	-	-	12.363%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-10-09T01:59:41

kkmrkkblmbrbk

Manual testing

200000000

5000000000

skipped known factor: 59509753
skipped known factor: 1206346099687

0.369

-

-

12.363%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-08-26T19:59:00	ANONYMOUS	Manual testing	?	?	1206346099687	40.134	13	2.73641e-6	3.53908e-5	5.60145e-6

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-08-26T19:59:00

ANONYMOUS

Manual testing

1206346099687

40.134

2.73641e-6

3.53908e-5

5.60145e-6

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.209 GHz-days
Estimated T-Level:	34.782

Digits	B1	Curves	Complete	FacMiss
20	11000	2377 / 100	23.770	0.000%
25	50000	2377 / 280	8.489	0.020%
30	250000	2096 / 640	3.275	3.772%
35	1000000	1511 / 1580	0.956	38.418%

New Calculation Method

Total ECM effort:	19.209 GHz-days
Estimated T-Level:	34.782

Digits	B1	Complete	FacMiss
20	11000	273.672	0.000%
25	50000	51.039	0.000%
30	250000	7.527	0.054%
35	1000000	0.888	41.142%
40	3000000	0.086	91.741%
45	11000000	0.007	99.282%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	0.161
250000	25000000		585	1.681
1000000	100000000		1,453	16.70
1000000	100000000	677255057696161993076824730156639	58	0.667

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-30T14:35:00	Matthias Wurtinger	WUR_E6600	50000	5000000						30	0.017
2010-04-13T20:58:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-13T21:18:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-14T02:37:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-14T15:15:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-14T21:39:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-15T02:41:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-15T07:57:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-15T13:06:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-24T03:15:00	James Hintz	home2	50000	5000000						163	0.094
2011-01-20T20:17:00	James Hintz	NEW_OMFG	250000	25000000						4	0.011
2011-03-17T01:32:00	James Hintz	17_051310	250000	25000000						11	0.032
2015-06-20T15:50:00	James Hintz	08_04_2014	250000	25000000						570	1.638
2015-06-20T16:16:00	James Hintz	08_04_2014	1000000	100000000						11	0.126
2017-06-12T03:51:09	nordi	nordiputer	1000000	100000000	677255057696161993076824730156639	109.061	58	2		58	0.667
2017-06-15T23:24:27	nordi	nordiputer	1000000	100000000						1442	16.57

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:41:47

Oliver Kruse

Ollaptop

59509753

1206346099687

677255057696161993076824730156639

D7E1BD90DB0FAEB3

2017-09-21T21:29:02

Oliver Kruse

Manual testing

59509753

1206346099687

677255057696161993076824730156639

D7E1BD90DB0FAEB3

2017-10-02T10:35:57

kkmrkkblmbrbk

Manual testing

59509753

1206346099687

677255057696161993076824730156639

D7E1BD90DB0FAE__

2017-12-07T03:12:55

ATH

xps

59509753

1206346099687

677255057696161993076824730156639

D7E1BD90DB0FAE__

2020-04-17T13:47:35

Oliver Kruse

Manual testing

59509753

1206346099687

677255057696161993076824730156639

A52F5D304E43CA__

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 = 200000000, B2 = 5000000000 (P-1 stage 2)

B1 = 200000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

10²²

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