M3511687 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	16.9733	67.6471%	1000000	145208700	1.3488	7.7908%	18.3221	70.1676%	2.5206%
PrimeNet	2⁶⁰	0.0437	63.3333%	15000	300000	0.0046	2.9622%	0.0484	64.4195%	1.0861%
GPU72	2⁶⁴	1.0136	65.6250%	20000	360000	0.0059	1.9166%	1.0194	66.2838%	0.6588%
Difference	+4	+15.9597	+2.0221%	+980000	+144848700	+1.3430	+5.8742%	+17.3027	+3.8838%	+3.8838%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

16.9733

67.6471%

1000000

145208700

1.3488

7.7908%

18.3221

70.1676%

2.5206%

PrimeNet

2⁶⁰

0.0437

63.3333%

15000

300000

0.0046

2.9622%

0.0484

64.4195%

1.0861%

GPU72

2⁶⁴

1.0136

65.6250%

20000

360000

0.0059

1.9166%

1.0194

66.2838%

0.6588%

Difference

+15.9597

+2.0221%

+980000

+144848700

+1.3430

+5.8742%

+17.3027

+3.8838%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3511687	13091399956967089	17	53.539	1863975912 2³ × 3 × 67 × 1159189	-	67	1159189	0.0007	0.0096	0.0180

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3511687

13091399956967089

53.539

1863975912
2³ × 3 × 67 × 1159189

1159189

0.0007

0.0096

0.0180

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2020-10-11T01:34:49	Jocelyn Larouche	Manual testing	351168	3511687	6	-	skipped known factor: 13091399956967089	-	-	0.080	-	-	3.522%
2022-04-24T23:35:31	Jocelyn Larouche	Manual testing	1000000	145208700		-	skipped known factor: 13091399956967089	-	-	1.349	-	-	7.791%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2022-01-31T09:35:50	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.512	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.443 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:	0.443 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		3	0.443

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-11-04T13:32:43	rucio		50000	5000000						3	0.443

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-08T02:12:14

Oliver Kruse

GTX-3

13091399956967089

B458A7E09DCEB0__

2017-12-17T01:08:04

LookAS

home

13091399956967089

B458A7E09DCEB0__

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 = 1000000, B2 = 145208700 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 351168, B2 = 3511687 (P-1 stage 2)

B1 = 351168 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

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