M6173767 Mersenne number exponent details

Residue

Status

L-L

525484EF17458A09

double-checked

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	4.8129	65.6716%	115000	2242500	0.0593	3.2758%	4.8723	66.7962%	1.1245%
PrimeNet	2⁶²	0.0995	62.9032%	26000	600000	0.0147	3.3452%	0.1142	64.1442%	1.2410%
GPU72	2⁶⁶	2.3921	65.1515%	40000	900000	0.0223	2.4286%	2.4144	65.9978%	0.8463%
Difference	+1	+2.4208	+0.5201%	+75000	+1342500	+0.0370	+0.8472%	+2.4578	+0.7983%	+0.7983%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

4.8129

65.6716%

115000

2242500

0.0593

3.2758%

4.8723

66.7962%

1.1245%

PrimeNet

2⁶²

0.0995

62.9032%

26000

600000

0.0147

3.3452%

0.1142

64.1442%

1.2410%

GPU72

2⁶⁶

2.3921

65.1515%

40000

900000

0.0223

2.4286%

2.4144

65.9978%

0.8463%

Difference

+2.4208

+0.5201%

+75000

+1342500

+0.0370

+0.8472%

+2.4578

+0.7983%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6173767	154816361359008361577	21	67.069	12538241349164 2² × 775193 × 4043587	2011-09-10	775193	4043587	9.3234	0.2450	0.4054
6173767	180535102970857216601	21	67.291	14621146454900 2² × 5² × 331 × 1451 × 304429	2022-03-18	1451	304429	9.2354	0.0046	0.0080

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

6173767

154816361359008361577

67.069

12538241349164
2² × 775193 × 4043587

2011-09-10

775193

4043587

9.3234

0.2450

0.4054

6173767

180535102970857216601

67.291

14621146454900
2² × 5² × 331 × 1451 × 304429

2022-03-18

1451

304429

9.2354

0.0046

0.0080

exponent	prime factors	composite factor	digits	bits*
6173767	154816361359008361577 180535102970857216601	27949787739522014849458043472131614939777	41	134.360

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-12-07T00:00:00	ANONYMOUS	v4_computers	25000	25000		-		-	-	0.006	-	-	0.458%
2011-04-29T21:47:00	markr	tiny	115000	2242500		-	MISSED FACTOR!	-	-	0.059	-	-	3.276%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-10-04T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.100	-	-
2022-03-19T22:26:35	LordJulius	Manual testing	2⁶²	2⁶⁴		-	-	0.477	-	-
2022-03-19T22:26:35	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	0.605	-	-
2022-03-19T22:26:35	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	1.210	-	-
2022-03-19T22:26:35	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	2.421	-	-
2022-03-18T07:53:31	TJAOI	Manual testing	2⁶⁷	2⁶⁸*	180535102970857216601	67.291	21	4.422	2.225	8.994

ECM factoring results:

Old Calculation Method

Total ECM effort:

0.000 GHz-days

Digits	B1	Curves	Complete	FacMiss

New Calculation Method

Total ECM effort:

0.000 GHz-days

Digits	B1	Complete	FacMiss

ECM Summary

B1	B2	factor	curves	GHz-days
		154816361359008361577	1	0.00000e+0

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-09-10T15:02:00	JimBa	Dell			154816361359008361577	67.069		1		1	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-11-14T00:00:00	ANONYMOUS	v4_computers	525484EF17458A09	1.094
2001-02-18T00:00:00	ANONYMOUS	v4_computers	525484EF17458A09	1.094

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-02T00:28:11

kkmrkkblmbrbk

c4.xlarge

154816361359008361577

8BF09B89B51493__

2018-09-19T05:31:40

ANONYMOUS

154816361359008361577

8BF09B89B51493__

2022-03-24T13:10:27

Poao

office-CN3

154816361359008361577

180535102970857216601

DC69459EA8E75971

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 = 115000, B2 = 2242500 (P-1 stage 2)

B1 = 115000 (P-1 stage 1)

B1 = 25000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶²

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