M31531 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	unknown	200000000	5000000000	0.3686	48.9156%	0.3686	48.9156%	48.9156%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	4.1558%	0.0000	64.0584%	1.5584%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.7845%	0.0001	66.5174%	0.6083%
Difference	-44	-0.0001	-65.9091%	+199999500	+4999990000	+0.3686	+47.1311%	+0.3685	-17.6018%	-17.6018%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

unknown

200000000

5000000000

0.3686

48.9156%

0.3686

48.9156%

PrimeNet

2⁴⁰

0.0000

62.5000%

500

10000

0.0000

4.1558%

0.0000

64.0584%

1.5584%

GPU72

2⁴⁴

0.0001

65.9091%

500

10000

0.0000

1.7845%

0.0001

66.5174%

0.6083%

Difference

-44

-0.0001

-65.9091%

+199999500

+4999990000

+0.3686

+47.1311%

+0.3685

-17.6018%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
31531	432857569	9	28.689	6864 2⁴ × 3 × 11 × 13	-	16	16	1.685e-9	1.278e-8	2.601e-8
31531	120481561651650369509914507935137	33	106.571	1910525540763857307251823728 2⁴ × 67 × 12621901 × 141199543647214049	2017-07-20	12621901	141199543647214049	4.895e+12	6,144,416	11,476,058

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

31531

432857569

28.689

6864
2⁴ × 3 × 11 × 13

1.685e-9

1.278e-8

2.601e-8

31531

120481561651650369509914507935137

106.571

1910525540763857307251823728
2⁴ × 67 × 12621901 × 141199543647214049

2017-07-20

12621901

141199543647214049

4.895e+12

6,144,416

11,476,058

exponent	prime factors	composite factor	digits	bits*
31531	432857569 120481561651650369509914507935137	52151355885857003784013315302634611501953	41	135.260

exponent

prime factors

composite factor

digits

bits*

31531

432857569
120481561651650369509914507935137

52151355885857003784013315302634611501953

135.260

	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: 432857569	-	-	0.369	-	-	41.267%

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: 432857569

0.369

-

-

41.267%

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		511	5.873
1000000	100000000	120481561651650369509914507935137	1,000	11.49

	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
2010-04-15T16:45:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-15T17:37:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-15T18:25:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-15T19:17:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-15T21:20:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-15T22:11:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-15T23:01:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-24T13:13:00	James Hintz	home2	50000	5000000						174	0.100
2011-01-20T20:59:00	James Hintz	NEW_OMFG	250000	25000000						4	0.011
2011-03-16T21:11:00	James Hintz	17_051310	250000	25000000						11	0.032
2015-06-22T18:39:00	James Hintz	08_04_2014	250000	25000000						570	1.638
2015-06-22T19:16:00	James Hintz	08_04_2014	1000000	100000000						11	0.126
2017-07-20T23:21:27	nordi	nordiputer	1000000	100000000	120481561651650369509914507935137	106.571	1000	2		1000	11.49
2017-07-21T19:41:23	nordi	nordiputer	1000000	100000000						400	4.597
2017-08-07T23:05:50	nordi	nordiputer	1000000	100000000						100	1.149

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:41:50

Oliver Kruse

Oliver-PC

E47E53D4164117__

2017-09-21T20:27:24

Oliver Kruse

Manual testing

E47E53D4164117__

2017-10-02T10:35:57

kkmrkkblmbrbk

Manual testing

432857569

120481561651650369509914507935137

E47E53D4164117__

2017-12-07T03:12:58

ATH

xps

432857569

120481561651650369509914507935137

E47E53D4164117__

2020-04-17T13:47:34

Oliver Kruse

Manual testing

432857569

120481561651650369509914507935137

302C52F20704BC__

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

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