M10040491 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

0AEF51130CAA56__

unverified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁹	11.8905	65.2174%	-	-	-	-	11.8905	65.2174%	0.0000%
PrimeNet	2⁶⁴	0.3545	62.5000%	45000	1300000	0.0479	3.7467%	0.4024	63.9050%	1.4050%
GPU72	2⁶⁸	5.9365	64.7059%	65000	1500000	0.0606	2.5695%	5.9970	65.6128%	0.9069%
Difference	+1	+5.9541	+0.5115%	-65000	-1500000	-0.0606	-2.5695%	+5.8935	-0.3954%	-0.3954%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

11.8905

65.2174%

11.8905

65.2174%

0.0000%

PrimeNet

2⁶⁴

0.3545

62.5000%

45000

1300000

0.0479

3.7467%

0.4024

63.9050%

1.4050%

GPU72

2⁶⁸

5.9365

64.7059%

65000

1500000

0.0606

2.5695%

5.9970

65.6128%

0.9069%

Difference

+5.9541

+0.5115%

-65000

-1500000

-0.0606

-2.5695%

+5.8935

-0.3954%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
10040491	180728839	9	27.429	9 3²	-	9	9	1.784e-12	3.806e-6	7.746e-6
10040491	170788751911	12	37.313	8505 3⁵ × 5 × 7	2008-09-08	243	243	3.357e-9	0.0001	0.0002
10040491	13433132927664839	17	53.577	668948009 12503 × 53503	2014-09-30	12503	53503	0.0002	0.0062	0.0108

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

10040491

180728839

27.429

9
3²

1.784e-12

3.806e-6

7.746e-6

10040491

170788751911

37.313

8505
3⁵ × 5 × 7

2008-09-08

243

3.357e-9

0.0001

0.0002

10040491

13433132927664839

53.577

668948009
12503 × 53503

2014-09-30

12503

53503

0.0002

0.0062

0.0108

exponent	prime factors	composite factor	digits	bits*
10040491	180728839 170788751911	30866452847134061329	20	64.743
10040491	180728839 13433132927664839	2427754518149537333591921	25	81.006
10040491	170788751911 13433132927664839	2294228006970435296528757329	28	90.890
10040491	180728839 170788751911 13433132927664839	414633164101050678466263042182911031	36	118.319

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-08T05:40:00	Will Edgington	Manual testing	?	?	170788751911	37.313	12	1.53344e-9	6.307	3.30273e-9
2014-09-30T11:37:00	TJAOI	Manual testing	2⁵³	2⁵⁴*	13433132927664839	53.577	17	0.000	6.307	0.000
TF assumed completed to 67 but no detailed record exists
2021-11-24T10:53:59	ViliamF	Manual testing	2⁶⁷	2⁶⁸		-	-	2.977	-	-
2021-12-28T17:29:11	ViliamF	Manual testing	2⁶⁸	2⁶⁹		-	-	5.954	-	-

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-12-19T10:48:45

Niels_Mache_Nextcloud

SuperDry-X

180728839

170788751911

13433132927664839

0AEF51130CAA56__

2021-02-26T20:07:10

oodaira

com2

180728839

170788751911

13433132927664839

0AEF51130CAA5608

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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁰

10¹

10²

10³

10⁴

10⁵

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁵⁴

2²⁰

2³⁰

2⁴⁰

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