M3436507 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	17.3446	67.6471%	1000000	126668850	1.1950	7.6237%	18.5396	70.1135%	2.4665%
PrimeNet	2⁶⁰	0.0447	63.3333%	15000	280000	0.0045	2.8994%	0.0492	64.3964%	1.0631%
GPU72	2⁶⁴	1.0357	65.6250%	19000	340000	0.0056	1.8534%	1.0413	66.2621%	0.6371%
Difference	+4	+16.3089	+2.0221%	+981000	+126328850	+1.1894	+5.7703%	+17.4983	+3.8514%	+3.8514%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

17.3446

67.6471%

1000000

126668850

1.1950

7.6237%

18.5396

70.1135%

2.4665%

PrimeNet

2⁶⁰

0.0447

63.3333%

15000

280000

0.0045

2.8994%

0.0492

64.3964%

1.0631%

GPU72

2⁶⁴

1.0357

65.6250%

19000

340000

0.0056

1.8534%

1.0413

66.2621%

0.6371%

Difference

+16.3089

+2.0221%

+981000

+126328850

+1.1894

+5.7703%

+17.4983

+3.8514%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3436507	137314709563481	15	46.964	19978820 2² × 5 × 998941	-	5	998941	3.873e-6	0.0083	0.0155

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3436507

137314709563481

46.964

19978820
2² × 5 × 998941

998941

3.873e-6

0.0083

0.0155

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-01-21T00:59:35	Jocelyn Larouche	Manual testing	90000	90000			137314709563481	15	46.964	0.014	0.722	0.027	0.820%
2022-04-10T23:56:36	Jocelyn Larouche	Manual testing	1000000	126668850		-	skipped known factor: 137314709563481	-	-	1.195	-	-	7.624%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2021-06-10T14:05:05	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.698	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.441 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:	0.441 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	0.441

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-11-01T17:03:50	rucio		50000	5000000						3	0.441

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-06T08:29:05

kkmrkkblmbrbk

c4.xlarge

137314709563481

44035C2488BA88__

2017-11-21T23:23:26

Oliver Kruse

Threadripper

137314709563481

44035C2488BA88__

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 = 126668850 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 90000 (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