M45721331 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	2⁷⁰	5.2262	62.8571%	490000	10657500	2.4295	5.2301%	7.6557	64.7997%	1.9426%
PrimeNet	2⁶⁸	1.3037	61.7647%	200000	8000000	1.4544	5.4208%	2.7581	63.8374%	2.0726%
GPU72	2⁷²	20.9166	63.8889%	320000	10000000	1.9721	4.0296%	22.8886	65.3440%	1.4551%
Difference	-2	-15.6903	-1.0317%	+170000	+657500	+0.4574	+1.2005%	-15.2329	-0.5443%	-0.5443%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁰

5.2262

62.8571%

490000

10657500

2.4295

5.2301%

7.6557

64.7997%

1.9426%

PrimeNet

2⁶⁸

1.3037

61.7647%

200000

8000000

1.4544

5.4208%

2.7581

63.8374%

2.0726%

GPU72

2⁷²

20.9166

63.8889%

320000

10000000

1.9721

4.0296%

22.8886

65.3440%

1.4551%

Difference

-2

-15.6903

-1.0317%

+170000

+657500

+0.4574

+1.2005%

-15.2329

-0.5443%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
45721331	2068776071860350403687	22	70.809	22623751612353 3 × 61 × 90031 × 1373161	2012-09-10	90031	1373161	7.3692	0.3722	0.4264

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

45721331

2068776071860350403687

70.809

22623751612353
3 × 61 × 90031 × 1373161

2012-09-10

90031

1373161

7.3692

0.3722

0.4264

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2012-09-10T16:51:00	Jwb52z	Clay	490000	10657500			2068776071860350403687	22	70.809	2.430	146.8	4.859	5.230%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-12-14T00:00:00	Jocelyn Larouche	v4_computers	2¹	2⁵⁴		-	-	5.24886e-5	-	-
2007-02-20T00:00:00	1997rj7	v4_computers	2¹	2⁶³		-	-	0.035	-	-
2007-12-31T00:00:00	RMAC9.5	v4_computers	2¹	2⁶⁸		-	-	1.304	-	-
2011-10-26T20:06:00	Dubslow	Manual testing	2⁶⁸	2⁶⁹		-	-	1.308	-	-
2011-10-26T20:06:00	Dubslow	Manual testing	2⁶⁹	2⁷⁰		-	-	2.615	-	-

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 = 490000, B2 = 10657500 (P-1 stage 2)

B1 = 490000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶³

2⁵⁴

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