M3387317 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	2⁶⁸	17.5965	67.6471%	3387317	111907950	1.4163	8.3322%	19.0128	70.3428%	2.6957%
PrimeNet	2⁶⁰	0.0453	63.3333%	14000	280000	0.0043	2.8453%	0.0497	64.3766%	1.0433%
GPU72	2⁶⁴	1.0508	65.6250%	18000	320000	0.0052	1.7908%	1.0560	66.2406%	0.6156%
Difference	+4	+16.5457	+2.0221%	+3369317	+111587950	+1.4110	+6.5415%	+17.9567	+4.1022%	+4.1022%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

17.5965

67.6471%

3387317

111907950

1.4163

8.3322%

19.0128

70.3428%

2.6957%

PrimeNet

2⁶⁰

0.0453

63.3333%

14000

280000

0.0043

2.8453%

0.0497

64.3766%

1.0433%

GPU72

2⁶⁴

1.0508

65.6250%

18000

320000

0.0052

1.7908%

1.0560

66.2406%

0.6156%

Difference

+16.5457

+2.0221%

+3369317

+111587950

+1.4110

+6.5415%

+17.9567

+4.1022%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3387317	13139720556249719	17	53.545	1939546927 39317 × 49331	-	39317	49331	0.0005	0.0061	0.0122
3387317	120268549516131548839	21	66.705	17752774469607 3³ × 29 × 89 × 254750161	2018-10-19	89	254750161	6.7351	2.1137	3.9478

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3387317

13139720556249719

53.545

1939546927
39317 × 49331

39317

49331

0.0005

0.0061

0.0122

3387317

120268549516131548839

66.705

17752774469607
3³ × 29 × 89 × 254750161

2018-10-19

254750161

6.7351

2.1137

3.9478

exponent	prime factors	composite factor	digits	bits*
3387317	13139720556249719 120268549516131548839	1580295132347450907796545088728526241	37	120.250

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-03-14T12:32:31	Jocelyn Larouche	Manual testing	338731	3726048	6	-	skipped known factor: 13139720556249719	-	-	0.080	-	-	3.539%
2021-03-14T18:15:36	Jocelyn Larouche	Manual testing	338731	7113365	6	-	skipped known factor: 13139720556249719	-	-	0.108	-	-	4.077%
2021-12-28T19:52:00	Jocelyn Larouche	Manual testing	3387317	3387317		-	skipped known factor: 13139720556249719	-	-	0.516	-	-	3.898%
2021-12-29T13:07:59	Jocelyn Larouche	Manual testing	3387317	111907950		-	skipped known factor: 13139720556249719	-	-	1.416	-	-	8.332%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2021-10-24T13:13:39	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.824	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.586 GHz-days
Estimated T-Level:	0.200

Digits	B1	Curves	Complete	FacMiss
20	11000	4 / 100	0.040	96.060%
25	50000	4 / 280	0.014	98.579%

New Calculation Method

Total ECM effort:	0.586 GHz-days
Estimated T-Level:	0.200

Digits	B1	Complete	FacMiss
20	11000	0.129	87.895%
25	50000	0.012	98.841%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.439
50000	5000000	120268549516131548839	1	0.146

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-10-19T06:39:30	MarkS	laptop64	50000	5000000	120268549516131548839	66.705	1	2		1	0.146
2019-08-23T10:10:08	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						3	0.439

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-05T18:23:03

Oliver Kruse

GTX-3

13139720556249719

1502BE9CEC1FC5__

2017-12-15T20:55:27

kkmrkkblmbrbk

c4.xlarge

13139720556249719

1502BE9CEC1FC5__

2018-10-21T04:59:12

J.R. Allen

Manual testing

13139720556249719

120268549516131548839

1502BE9CEC1FC5__

2018-10-21T12:05:41

Oliver Kruse

GTX-5

13139720556249719

120268549516131548839

1502BE9CEC1FC5__

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 = 3387317, B2 = 111907950 (P-1 stage 2)

B1 = 3387317 (P-1 stage 1)

B1 = 338731, B2 = 7113365 (P-1 stage 2)

B1 = 338731, B2 = 3726048 (P-1 stage 2)

B1 = 338731 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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