M67058449 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	2⁷¹	7.1293	63.3803%	725000	725000	2.6573	2.4824%	9.7866	64.2893%	0.9090%
PrimeNet	2⁷⁰	3.5633	62.8571%	280000	13000000	3.5664	5.3195%	7.1297	64.8329%	1.9758%
GPU72	2⁷⁴	57.0527	64.8649%	450000	15000000	4.5549	3.9288%	61.6076	66.2453%	1.3804%
Difference	-3	-49.9234	-1.4846%	+275000	-14275000	-1.8976	-1.4465%	-51.8210	-1.9559%	-1.9559%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷¹

7.1293

63.3803%

725000

2.6573

2.4824%

9.7866

64.2893%

0.9090%

PrimeNet

2⁷⁰

3.5633

62.8571%

280000

13000000

3.5664

5.3195%

7.1297

64.8329%

1.9758%

GPU72

2⁷⁴

57.0527

64.8649%

450000

15000000

4.5549

3.9288%

61.6076

66.2453%

1.3804%

Difference

-3

-49.9234

-1.4846%

+275000

-14275000

-1.8976

-1.4465%

-51.8210

-1.9559%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
67058449	12003053851265177348924609	26	83.312	89496954002508896 2⁵ × 71 × 349 × 259841 × 434377	2013-08-21	259841	434377	32,601	0.9872	1.9383

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

67058449

12003053851265177348924609

83.312

89496954002508896
2⁵ × 71 × 349 × 259841 × 434377

2013-08-21

259841

434377

32,601

0.9872

1.9383

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2013-08-21T09:18:00	Jwb52z	Clay	725000	725000			12003053851265177348924609	26	83.312	2.657	339.0	5.315	2.482%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-12-11T07:40:00	Wojciech Florek	Manual testing	2¹	2⁶⁴		-	-	0.053	-	-
2022-03-30T15:48:23	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	0.056	-	-
2010-03-05T23:56:00	Sturle Sunde	agrell.ifi	2⁶⁵	2⁶⁶		-	-	0.111	-	-
2010-03-07T09:03:00	unconnected	uae-5	2⁶⁶	2⁶⁷		-	-	0.223	-	-
2010-03-07T21:57:00	Sturle Sunde	kinner.ifi	2⁶⁷	2⁶⁸		-	-	0.446	-	-
2010-03-09T12:20:00	UCLA Mathematics	picprime	2⁶⁸	2⁶⁹		-	-	0.891	-	-
2012-02-13T17:33:00	nineaxe	collette	2⁶⁹	2⁷⁰		-	-	1.783	-	-
2012-07-12T00:18:00	ITS	ChrysalisTwo	2⁷⁰	2⁷¹		-	-	3.566	-	-

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 = 725000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁴

10⁵

10⁶

TF factor-bounds graph:

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

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