M67029509 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	7.1324	63.3803%	725000	16131250	5.7339	5.6040%	12.8662	65.4325%	2.0522%
PrimeNet	2⁷⁰	3.5649	62.8571%	280000	13000000	3.5664	5.3192%	7.1312	64.8328%	1.9757%
GPU72	2⁷⁴	57.0773	64.8649%	450000	15000000	4.5549	3.9286%	61.6323	66.2452%	1.3803%
Difference	-3	-49.9450	-1.4846%	+275000	+1131250	+1.1789	+1.6754%	-48.7660	-0.8127%	-0.8127%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷¹

7.1324

63.3803%

725000

16131250

5.7339

5.6040%

12.8662

65.4325%

2.0522%

PrimeNet

2⁷⁰

3.5649

62.8571%

280000

13000000

3.5664

5.3192%

7.1312

64.8328%

1.9757%

GPU72

2⁷⁴

57.0773

64.8649%

450000

15000000

4.5549

3.9286%

61.6323

66.2452%

1.3803%

Difference

-3

-49.9450

-1.4846%

+275000

+1131250

+1.1789

+1.6754%

-48.7660

-0.8127%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
67029509	5347973969691118904158777	25	82.145	39892683457453932 2² × 3³ × 7 × 641 × 92767 × 887401	2013-08-13	92767	887401	27,365	0.4987	0.6920

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

67029509

5347973969691118904158777

82.145

39892683457453932
2² × 3³ × 7 × 641 × 92767 × 887401

2013-08-13

92767

887401

27,365

0.4987

0.6920

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2013-08-13T06:15:00	Jwb52z	Clay	725000	16131250			5347973969691118904158777	25	82.145	5.734	338.9	11.47	5.604%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2002-10-26T00:00:00	Jocelyn Larouche	v4_computers	2¹	2⁶⁰		-	-	0.002	-	-
2022-03-30T15:48:22	LordJulius	Manual testing	2⁶⁰	2⁶³		-	-	0.022	-	-
2008-12-10T23:04:00	Wojciech Florek	Manual testing	2⁶³	2⁶⁴		-	-	0.029	-	-
2009-05-02T22:34:00	RMAC9.5	AMD-X2-6400	2⁶⁴	2⁶⁵		-	-	0.056	-	-
2009-12-27T20:21:00	Sturle Sunde	doak.ifi	2⁶⁵	2⁶⁶		-	-	0.111	-	-
2010-03-10T03:02:00	ANONYMOUS		2⁶⁶	2⁶⁷		-	-	0.223	-	-
2010-03-12T11:35:00	ANONYMOUS		2⁶⁷	2⁶⁸		-	-	0.446	-	-
2010-03-18T08:21:00	ANONYMOUS		2⁶⁸	2⁶⁹		-	-	0.892	-	-
2012-02-17T10:21:00	Per Jessen	louiswu6	2⁶⁹	2⁷⁰		-	-	1.784	-	-
2012-10-10T00:13:00	Clown_Royal	Manual testing	2⁷⁰	2⁷¹		-	-	3.567	-	-

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, B2 = 16131250 (P-1 stage 2)

B1 = 725000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶⁰

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