M31039 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	48.8887%	0.3686	48.8887%	48.8887%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	4.1392%	0.0000	64.0522%	1.5522%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.7763%	0.0001	66.5146%	0.6055%
Difference	-44	-0.0001	-65.9091%	+199999500	+4999990000	+0.3686	+47.1124%	+0.3685	-17.6259%	-17.6259%

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

48.8887%

0.3686

48.8887%

PrimeNet

2⁴⁰

0.0000

62.5000%

500

10000

0.0000

4.1392%

0.0000

64.0522%

1.5522%

GPU72

2⁴⁴

0.0001

65.9091%

500

10000

0.0000

1.7763%

0.0001

66.5146%

0.6055%

Difference

-44

-0.0001

-65.9091%

+199999500

+4999990000

+0.3686

+47.1124%

+0.3685

-17.6259%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
31039	217444023958831	15	47.628	3502754985 3 × 5 × 23² × 73 × 6047	-	529	6047	0.0006	6.626e-7	8.599e-7
31039	41418462577279318406682236918087	32	105.030	667200337918092052042305437 1901 × 36640169197 × 9578922736021	2017-05-11	36640169197	9578922736021	5.594e+12	444.51	778.53

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

31039

217444023958831

47.628

3502754985
3 × 5 × 23² × 73 × 6047

529

6047

0.0006

6.626e-7

8.599e-7

31039

41418462577279318406682236918087

105.030

667200337918092052042305437
1901 × 36640169197 × 9578922736021

2017-05-11

36640169197

9578922736021

5.594e+12

444.51

778.53

exponent	prime factors	composite factor	digits	bits*
31039	217444023958831 41418462577279318406682236918087	9006197168991869280482241825305494650407276297	46	152.658

exponent

prime factors

composite factor

digits

bits*

31039

217444023958831
41418462577279318406682236918087

9006197168991869280482241825305494650407276297

152.658

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-10-09T01:59:40	kkmrkkblmbrbk	Manual testing	200000000	5000000000	12	-	skipped known factor: 217444023958831	-	-	0.369	-	-	41.238%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-10-09T01:59:40

kkmrkkblmbrbk

Manual testing

200000000

5000000000

skipped known factor: 217444023958831

0.369

-

-

41.238%

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		1,132	13.01
1000000	100000000	41418462577279318406682236918087	379	4.356

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-30T14:33:00	Matthias Wurtinger	WUR_E6600	50000	5000000						30	0.017
2010-04-13T18:11:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-13T18:29:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-13T23:48:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-14T05:08:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-14T17:46:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-15T00:00:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-15T05:11:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-15T10:19:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-22T22:07:00	James Hintz	home2	50000	5000000						163	0.094
2011-01-20T17:03:00	James Hintz	NEW_OMFG	250000	25000000						4	0.011
2011-03-17T07:52:00	James Hintz	17_051310	250000	25000000						11	0.032
2015-05-13T21:14:00	James Hintz	08_04_2014	250000	25000000						570	1.638
2015-05-13T21:59:00	James Hintz	08_04_2014	1000000	100000000						11	0.126
2017-05-11T21:20:38	nordi	nordiputer	1000000	100000000	41418462577279318406682236918087	105.030	379	2		379	4.356
2017-05-31T00:35:46	nordi	nordiputer	1000000	100000000						1121	12.88

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:41:14

Oliver Kruse

Ollaptop

FC5523194B0A6D__

2017-09-21T21:38:48

Oliver Kruse

Manual testing

FC5523194B0A6D__

2017-10-02T10:35:43

kkmrkkblmbrbk

Manual testing

217444023958831

41418462577279318406682236918087

FC5523194B0A6D__

2017-12-07T03:12:46

ATH

xps

217444023958831

41418462577279318406682236918087

FC5523194B0A6D__

2020-04-17T13:47:56

Oliver Kruse

Manual testing

217444023958831

41418462577279318406682236918087

27DB628927B75F__

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)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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