M3811369 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	2⁶⁷	7.7961	67.1642%	100000	130364850	1.0961	6.0216%	8.8922	69.1414%	1.9772%
PrimeNet	2⁶⁰	0.0403	63.3333%	17000	340000	0.0053	3.1895%	0.0456	64.5028%	1.1695%
GPU72	2⁶⁴	0.9339	65.6250%	24000	450000	0.0072	2.1643%	0.9411	66.3690%	0.7440%
Difference	+3	+6.8623	+1.5392%	+76000	+129914850	+1.0889	+3.8572%	+7.9511	+2.7724%	+2.7724%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

7.7961

67.1642%

100000

130364850

1.0961

6.0216%

8.8922

69.1414%

1.9772%

PrimeNet

2⁶⁰

0.0403

63.3333%

17000

340000

0.0053

3.1895%

0.0456

64.5028%

1.1695%

GPU72

2⁶⁴

0.9339

65.6250%

24000

450000

0.0072

2.1643%

0.9411

66.3690%

0.7440%

Difference

+6.8623

+1.5392%

+76000

+129914850

+1.0889

+3.8572%

+7.9511

+2.7724%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3811369	7981006687	10	32.894	1047 3 × 349	-	3	349	1.841e-10	3.328e-6	5.344e-6

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3811369

7981006687

32.894

1047
3 × 349

349

1.841e-10

3.328e-6

5.344e-6

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-03-03T20:34:47	Jocelyn Larouche	Manual testing	90000	90000		-	skipped known factor: 7981006687	-	-	0.014	-	-	0.964%
2022-03-22T01:43:08	Jocelyn Larouche	Manual testing	100000	100000		-	skipped known factor: 7981006687	-	-	0.015	-	-	1.024%
2022-06-01T22:48:32	Jocelyn Larouche	Manual testing	100000	130364850		-	skipped known factor: 7981006687	-	-	1.096	-	-	6.022%

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.450 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:	0.450 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	0.450

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-11-17T18:39:04	rucio		50000	5000000						3	0.450

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T19:21:53

kkmrkkblmbrbk

Manual testing

7981006687

A0E9B5009E619A__

2017-12-11T20:14:59

Oliver Kruse

GTX-2

7981006687

A0E9B5009E619A__

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 = 100000, B2 = 130364850 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

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