M2231371 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	13.3164	67.1642%	1000000	106000000	0.6407	7.7360%	13.9572	69.7044%	2.5402%
PrimeNet	2⁵⁸	0.0172	62.0690%	10000	180000	0.0018	2.8705%	0.0190	63.1578%	1.0888%
GPU72	2⁶²	0.2753	64.5161%	11000	180000	0.0019	1.6316%	0.2773	65.0951%	0.5789%
Difference	+5	+13.0411	+2.6481%	+989000	+105820000	+0.6388	+6.1045%	+13.6799	+4.6093%	+4.6093%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.3164

67.1642%

1000000

106000000

0.6407

7.7360%

13.9572

69.7044%

2.5402%

PrimeNet

2⁵⁸

0.0172

62.0690%

10000

180000

0.0018

2.8705%

0.0190

63.1578%

1.0888%

GPU72

2⁶²

0.2753

64.5161%

11000

180000

0.0019

1.6316%

0.2773

65.0951%

0.5789%

Difference

+13.0411

+2.6481%

+989000

+105820000

+0.6388

+6.1045%

+13.6799

+4.6093%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2231371	160658713	9	27.259	36 2² × 3²	-	9	9	8.076e-12	8.580e-7	1.746e-6
2231371	30253371963648330209	20	64.714	6779099478224 2⁴ × 83 × 5104743583	2017-12-27	83	5104743583	2.2635	26.515	49.523

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2231371

160658713

27.259

36
2² × 3²

8.076e-12

8.580e-7

1.746e-6

2231371

30253371963648330209

64.714

6779099478224
2⁴ × 83 × 5104743583

2017-12-27

5104743583

2.2635

26.515

49.523

exponent	prime factors	composite factor	digits	bits*
2231371	160658713 30253371963648330209	4860467803590023515976961017	28	91.973

exponent

prime factors

composite factor

digits

bits*

2231371

160658713
30253371963648330209

4860467803590023515976961017

91.973

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-04-12T11:51:44	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 160658713	-	-	0.123	-	-	5.191%
2021-06-30T06:04:57	Dylan Delgado	laptop-ryzen73700	1000000	106000000		-	skipped known factor: 160658713	-	-	0.641	-	-	7.736%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2017-12-27T15:33:34	TJAOI	Manual testing	2⁶⁴	2⁶⁵*	30253371963648330209	64.714	20	0.668	0.298	1.359

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.952 GHz-days
Estimated T-Level:	0.500

Digits	B1	Curves	Complete	FacMiss
20	11000	10 / 100	0.100	90.438%
25	50000	10 / 280	0.036	96.485%

New Calculation Method

Total ECM effort:	0.952 GHz-days
Estimated T-Level:	0.500

Digits	B1	Complete	FacMiss
20	11000	0.407	66.561%
25	50000	0.038	96.300%
30	250000	0.002	99.761%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.257
50000	6896510		7	0.694

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-01-21T15:23:00	Oliver Kruse	ECM-HTC	50000	5000000						3	0.257
2022-06-09T11:54:55	debrouxl	o9020	50000	6896510						7	0.694

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-10T09:18:34

Oliver Kruse

GTX-3

160658713

39923F74BF4BF4__

2017-11-20T13:33:20

kkmrkkblmbrbk

c4.xlarge

160658713

39923F74BF4BF4__

2017-12-29T21:44:34

Oliver Kruse

GTX-2

160658713

30253371963648330209

1D71F3A08F81E1__

2017-12-30T09:31:03

kkmrkkblmbrbk

c4.xlarge

160658713

30253371963648330209

1D71F3A08F81E1__

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 = 106000000 (P-1 stage 2)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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