M10045837 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	2⁶⁹	11.8842	65.2174%	-	-	-	-	11.8842	65.2174%	0.0000%
PrimeNet	2⁶⁴	0.3543	62.5000%	45000	1300000	0.0479	3.7470%	0.4023	63.9051%	1.4051%
GPU72	2⁶⁸	5.9333	64.7059%	65000	1500000	0.0606	2.5697%	5.9938	65.6128%	0.9069%
Difference	+1	+5.9509	+0.5115%	-65000	-1500000	-0.0606	-2.5697%	+5.8904	-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

11.8842

65.2174%

11.8842

65.2174%

0.0000%

PrimeNet

2⁶⁴

0.3543

62.5000%

45000

1300000

0.0479

3.7470%

0.4023

63.9051%

1.4051%

GPU72

2⁶⁸

5.9333

64.7059%

65000

1500000

0.0606

2.5697%

5.9938

65.6128%

0.9069%

Difference

+5.9509

+0.5115%

-65000

-1500000

-0.0606

-2.5697%

+5.8904

-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
10045837	5051992357778441	16	52.166	251447060 2² × 5 × 137 × 163 × 563	-	163	563	0.0001	7.815e-5	0.0001
10045837	12927716779442807	17	53.521	643436519 11 × 17 × 151 × 22787	2014-09-28	151	22787	0.0002	0.0006	0.0010

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

10045837

5051992357778441

52.166

251447060
2² × 5 × 137 × 163 × 563

163

563

0.0001

7.815e-5

0.0001

10045837

12927716779442807

53.521

643436519
11 × 17 × 151 × 22787

2014-09-28

151

22787

0.0002

0.0006

0.0010

exponent	prime factors	composite factor	digits	bits*
10045837	5051992357778441 12927716779442807	65310726373269180460132337123887	32	105.687

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-09-28T11:09:00	TJAOI	Manual testing	2⁵³	2⁵⁴*	12927716779442807	53.521	17	0.000	6.310	0.000
TF assumed completed to 67 but no detailed record exists
2021-11-24T10:54:04	ViliamF	Manual testing	2⁶⁷	2⁶⁸		-	-	2.975	-	-
2021-12-28T17:29:07	ViliamF	Manual testing	2⁶⁸	2⁶⁹		-	-	5.951	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.584 GHz-days
Estimated T-Level:	0.500

Digits	B1	Curves	Complete	FacMiss
20	11000	10 / 100	0.100	90.438%
25	50000	10 / 280	0.036	96.485%

New Calculation Method

Total ECM effort:	8.584 GHz-days
Estimated T-Level:	0.500

Digits	B1	Complete	FacMiss
20	11000	0.500	60.653%
25	50000	0.048	95.284%
30	250000	0.003	99.688%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	14400000		10	8.584

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2021-01-27T05:40:34	riccardo uberti	Colab_noGPU11	50000	14400000						10	8.584

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-12-22T14:32:05

Yuji Hasegawa

vj22m

5051992357778441

12927716779442807

B5CFE3BC53159A__

2021-01-22T14:31:08

Oliver Kruse

IOS-5

5051992357778441

12927716779442807

B5CFE3BC53159A14

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

10¹

10²

10³

10¹

10²

10³

10⁴

10⁵

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