M4835297 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	2⁶⁷	6.1452	65.6716%	-	-	-	-	6.1452	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0635	62.2951%	20000	450000	0.0083	3.2287%	0.0718	63.5124%	1.2174%
GPU72	2⁶⁵	1.5088	64.6154%	32000	650000	0.0125	2.3251%	1.5214	65.4381%	0.8227%
Difference	+2	+4.6364	+1.0563%	-32000	-650000	-0.0125	-2.3251%	+4.6238	+0.2335%	+0.2335%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.1452

65.6716%

6.1452

65.6716%

0.0000%

PrimeNet

2⁶¹

0.0635

62.2951%

20000

450000

0.0083

3.2287%

0.0718

63.5124%

1.2174%

GPU72

2⁶⁵

1.5088

64.6154%

32000

650000

0.0125

2.3251%

1.5214

65.4381%

0.8227%

Difference

+4.6364

+1.0563%

-32000

-650000

-0.0125

-2.3251%

+4.6238

+0.2335%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4835297	851012273	9	29.665	88 2³ × 11	-	8	11	1.507e-11	1.559e-6	3.108e-6
4835297	2481782141138069689	19	61.106	256631820252 2² × 3 × 19 × 1125578159	2016-04-01	19	1125578159	0.0662	11.708	21.867

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4835297

851012273

29.665

88
2³ × 11

1.507e-11

1.559e-6

3.108e-6

4835297

2481782141138069689

61.106

256631820252
2² × 3 × 19 × 1125578159

2016-04-01

1125578159

0.0662

11.708

21.867

exponent	prime factors	composite factor	digits	bits*
4835297	851012273 2481782141138069689	2112027061020715492868293097	28	90.771

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-04-01T11:30:34	TJAOI	Manual testing	2⁶¹	2⁶²*	2481782141138069689	61.106	19	0.003	1.294	0.005

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.596 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.596 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.596

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-06-20T15:24:04	ATH	ec2-ECMCF	50000	5000000						3	0.596

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T06:28:34

kkmrkkblmbrbk

Manual testing

851012273

2481782141138069689

02BE24D57E732F__

2018-03-29T15:40:08

Oliver Kruse

GTX-7

851012273

2481782141138069689

02BE24D57E732F__

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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁷

2⁶²

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