M3494417 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	2⁶⁹	34.1650	68.1159%	1000000	114656850	1.0953	6.9023%	35.2603	70.3167%	2.2007%
PrimeNet	2⁶⁰	0.0440	63.3333%	15000	300000	0.0046	2.9596%	0.0486	64.4185%	1.0852%
GPU72	2⁶⁴	1.0186	65.6250%	19000	360000	0.0057	1.8882%	1.0243	66.2741%	0.6491%
Difference	+5	+33.1464	+2.4909%	+981000	+114296850	+1.0896	+5.0141%	+34.2360	+4.0426%	+4.0426%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

34.1650

68.1159%

1000000

114656850

1.0953

6.9023%

35.2603

70.3167%

2.2007%

PrimeNet

2⁶⁰

0.0440

63.3333%

15000

300000

0.0046

2.9596%

0.0486

64.4185%

1.0852%

GPU72

2⁶⁴

1.0186

65.6250%

19000

360000

0.0057

1.8882%

1.0243

66.2741%

0.6491%

Difference

+33.1464

+2.4909%

+981000

+114296850

+1.0896

+5.0141%

+34.2360

+4.0426%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3494417	167732017	9	27.322	24 2³ × 3	-	8	8	5.143e-12	1.218e-6	2.479e-6

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3494417

167732017

27.322

24
2³ × 3

5.143e-12

1.218e-6

2.479e-6

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2020-11-24T09:30:53	Jocelyn Larouche	Manual testing	349441	3494417	6	-	skipped known factor: 167732017	-	-	0.079	-	-	3.162%
2021-12-23T11:28:04	Jocelyn Larouche	Manual testing	749441	129752700		-	skipped known factor: 167732017	-	-	1.184	-	-	6.789%
2022-01-22T13:05:01	Jocelyn Larouche	Manual testing	1000000	114656850		-	skipped known factor: 167732017	-	-	1.095	-	-	6.902%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2021-02-21T11:36:47	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.138	-	-
2021-02-23T01:24:33	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.277	-	-
2021-04-04T08:03:16	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.554	-	-
2021-12-18T19:15:40	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	17.11	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.442 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:	0.442 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	0.442

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-11-04T00:33:27	rucio		50000	5000000						3	0.442

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-07T14:46:11

Oliver Kruse

GTX-2

167732017

5884CC829CF20A__

2017-12-17T00:36:49

kkmrkkblmbrbk

c4.xlarge

167732017

5884CC829CF20A__

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 = 749441, B2 = 129752700 (P-1 stage 2)

B1 = 1000000, B2 = 114656850 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 749441 (P-1 stage 1)

B1 = 349441, B2 = 3494417 (P-1 stage 2)

B1 = 349441 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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