M4798537 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	6.1923	65.6716%	-	-	-	-	6.1923	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0640	62.2951%	20000	450000	0.0083	3.2245%	0.0723	63.5109%	1.2158%
GPU72	2⁶⁵	1.5204	64.6154%	32000	650000	0.0125	2.3221%	1.5329	65.4370%	0.8217%
Difference	+2	+4.6719	+1.0563%	-32000	-650000	-0.0125	-2.3221%	+4.6593	+0.2346%	+0.2346%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.1923

65.6716%

6.1923

65.6716%

0.0000%

PrimeNet

2⁶¹

0.0640

62.2951%

20000

450000

0.0083

3.2245%

0.0723

63.5109%

1.2158%

GPU72

2⁶⁵

1.5204

64.6154%

32000

650000

0.0125

2.3221%

1.5329

65.4370%

0.8217%

Difference

+4.6719

+1.0563%

-32000

-650000

-0.0125

-2.3221%

+4.6593

+0.2346%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4798537	3598902751	10	31.745	375 3 × 5³	-	125	125	6.446e-11	2.386e-5	4.857e-5
4798537	9549088631	10	33.153	995 5 × 199	2008-09-08	5	199	2.898e-10	2.973e-6	3.875e-6
4798537	7075807495313	13	42.686	737288 2³ × 23 × 4007	2008-09-30	23	4007	1.937e-7	4.583e-5	7.778e-5
4798537	517737293857769594857	21	68.811	53947410831444 2² × 3 × 13 × 17 × 41 × 73 × 607 × 11197	2019-05-29	607	11197	17.340	0.0002	0.0002

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4798537

3598902751

31.745

375
3 × 5³

125

6.446e-11

2.386e-5

4.857e-5

4798537

9549088631

33.153

995
5 × 199

2008-09-08

199

2.898e-10

2.973e-6

3.875e-6

4798537

7075807495313

42.686

737288
2³ × 23 × 4007

2008-09-30

4007

1.937e-7

4.583e-5

7.778e-5

4798537

517737293857769594857

68.811

53947410831444
2² × 3 × 13 × 17 × 41 × 73 × 607 × 11197

2019-05-29

607

11197

17.340

0.0002

exponent	prime factors	composite factor	digits	bits*
4798537	3598902751 9549088631	34366241343648723881	20	64.898
4798537	3598902751 7075807495313	25465143060428375306063	23	74.431
4798537	9549088631 7075807495313	67567512908637954086503	23	75.839
4798537	3598902751 517737293857769594857	1863286171160022397655012751607	31	100.556
4798537	9549088631 517737293857769594857	4943919306621933769266454770767	31	101.963
4798537	3598902751 9549088631 7075807495313	243168908085125144624927338669753	33	107.584
4798537	7075807495313 517737293857769594857	3663409424481875336249755936405241	34	111.497
4798537	3598902751 9549088631 517737293857769594857	17792684793323689959152843326530430680017	41	133.708
4798537	3598902751 7075807495313 517737293857769594857	13184254255807147897268296662607402885717991	44	143.242
4798537	9549088631 7075807495313 517737293857769594857	34982221286018128838941846588852045841915071	44	144.650
4798537	3598902751 9549088631 7075807495313 517737293857769594857	12589761242234140171434024761763959371244626013026 0321	54	176.394

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-30T21:36:00	markr	Manual testing	?	?	7075807495313	42.686	13	7.15684e-8	1.348	1.52722e-7
2008-09-08T00:13:00	Will Edgington	Manual testing	?	?	9549088631	33.153	10	5.13601e-11	1.348	1.09599e-10

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.396 GHz-days
Estimated T-Level:	0.100

Digits	B1	Curves	Complete	FacMiss
20	11000	2 / 100	0.020	98.010%
25	50000	2 / 280	0.007	99.287%

New Calculation Method

Total ECM effort:	0.396 GHz-days
Estimated T-Level:	0.100

Digits	B1	Complete	FacMiss
20	11000	0.077	92.596%
25	50000	0.007	99.291%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	517737293857769594857	2	0.396

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-05-29T12:10:39	ATH	ec2-ECMCF	50000	5000000	517737293857769594857	68.811	2	2	6341435520457984	2	0.396

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-19T13:05:50

kkmrkkblmbrbk

c4.xlarge

3598902751

9549088631

7075807495313

D4E26B95D36683__

2018-03-24T20:04:39

Oliver Kruse

GTX-1

3598902751

9549088631

7075807495313

D4E26B95D36683__

2019-05-30T02:49:11

Niels_Mache_Nextcloud

SuperDry-X

3598902751

9549088631

7075807495313

517737293857769594857

D4E26B95D3668362

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

10⁰

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