M3181163 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	18.7368	67.6471%	1050000	116447100	0.9055	7.5098%	19.6423	70.0767%	2.4297%
PrimeNet	2⁶⁰	0.0483	63.3333%	13000	240000	0.0031	2.6546%	0.0514	64.3067%	0.9734%
GPU72	2⁶⁴	1.1189	65.6250%	15000	260000	0.0035	1.5830%	1.1224	66.1692%	0.5442%
Difference	+4	+17.6179	+2.0221%	+1035000	+116187100	+0.9020	+5.9268%	+18.5199	+3.9076%	+3.9076%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

18.7368

67.6471%

1050000

116447100

0.9055

7.5098%

19.6423

70.0767%

2.4297%

PrimeNet

2⁶⁰

0.0483

63.3333%

13000

240000

0.0031

2.6546%

0.0514

64.3067%

0.9734%

GPU72

2⁶⁴

1.1189

65.6250%

15000

260000

0.0035

1.5830%

1.1224

66.1692%

0.5442%

Difference

+17.6179

+2.0221%

+1035000

+116187100

+0.9020

+5.9268%

+18.5199

+3.9076%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3181163	82710239	8	26.302	13 13	-	1	13	2.818e-12	2.041e-7	2.512e-7
3181163	1981101069881	13	40.849	311380 2² × 5 × 15569	2008-09-30	5	15569	6.438e-8	0.0001	0.0002
3181163	44985571498862380447	20	65.286	7070617176621 3 × 53 × 15607 × 2849317	2018-08-18	15607	2849317	3.0363	0.0210	0.0358

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3181163

82710239

26.302

13
13

2.818e-12

2.041e-7

2.512e-7

3181163

1981101069881

40.849

311380
2² × 5 × 15569

2008-09-30

15569

6.438e-8

0.0001

0.0002

3181163

44985571498862380447

65.286

7070617176621
3 × 53 × 15607 × 2849317

2018-08-18

15607

2849317

3.0363

0.0210

0.0358

exponent	prime factors	composite factor	digits	bits*
3181163	82710239 1981101069881	163857342973013211559	21	67.151
3181163	82710239 44985571498862380447	3720767370222495714880296833	28	91.588
3181163	1981101069881 44985571498862380447	89120963825604482677934155016807	32	106.136
3181163	82710239 1981101069881 44985571498862380447	7371216217926101081763293987703155986873	40	132.437

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2020-12-28T03:20:48	Jocelyn Larouche	Manual testing	318116	3181163	6	-	skipped known factor: 82710239 skipped known factor: 1981101069881 skipped known factor: 44985571498862380447	-	-	0.059	-	-	3.356%
2022-01-07T17:30:05	Jocelyn Larouche	Manual testing	1050000	116447100		-	skipped known factor: 82710239 skipped known factor: 1981101069881 skipped known factor: 44985571498862380447	-	-	0.905	-	-	7.510%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-30T14:46:00	markr	Manual testing	?	?	1981101069881	40.849	13	1.83381e-8	0.598	4.05021e-8
2021-09-13T11:19:39	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.396	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.352 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.352 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	44985571498862380447	3	0.352

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-08-18T16:58:29	ATH	ec2-ECMCF	50000	5000000	44985571498862380447	65.286	3	2		3	0.352

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-01T03:12:01

Oliver Kruse

GTX-1

82710239

1981101069881

ECC76C7ED16DFA__

2017-12-12T22:31:38

kkmrkkblmbrbk

c4.xlarge

82710239

1981101069881

ECC76C7ED16DFA__

2018-08-20T16:56:25

Oliver Kruse

GTX-1

82710239

1981101069881

44985571498862380447

ECC76C7ED16DFA__

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 = 1050000, B2 = 116447100 (P-1 stage 2)

B1 = 1050000 (P-1 stage 1)

B1 = 318116, B2 = 3181163 (P-1 stage 2)

B1 = 318116 (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