M4579657 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	6.4882	65.6716%	-	-	-	-	6.4882	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0671	62.2951%	19000	400000	0.0076	3.0735%	0.0747	63.4539%	1.1589%
GPU72	2⁶⁵	1.5931	64.6154%	28000	550000	0.0108	2.1371%	1.6038	65.3716%	0.7562%
Difference	+2	+4.8952	+1.0563%	-28000	-550000	-0.0108	-2.1371%	+4.8844	+0.3001%	+0.3001%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.4882

65.6716%

6.4882

65.6716%

0.0000%

PrimeNet

2⁶¹

0.0671

62.2951%

19000

400000

0.0076

3.0735%

0.0747

63.4539%

1.1589%

GPU72

2⁶⁵

1.5931

64.6154%

28000

550000

0.0108

2.1371%

1.6038

65.3716%

0.7562%

Difference

+4.8952

+1.0563%

-28000

-550000

-0.0108

-2.1371%

+4.8844

+0.3001%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4579657	27477943	8	24.712	3 3	-	1	3	4.884e-13	2.117e-7	3.885e-7
4579657	619792459753	12	39.173	67668 2² × 3 × 5639	2008-09-07	4	5639	2.633e-8	5.938e-5	0.0001
4579657	661483338308067761	18	59.198	72219746840 2³ × 5 × 41 × 397 × 110923	2015-11-03	397	110923	0.0308	0.0012	0.0022
4579657	944538983353845268839577	24	79.644	103123332528379884 2² × 3⁴ × 7 × 1039 × 43762118867	2019-02-08	1039	43762118867	39,372	455.20	850.18

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4579657

27477943

24.712

3
3

4.884e-13

2.117e-7

3.885e-7

4579657

619792459753

39.173

67668
2² × 3 × 5639

2008-09-07

5639

2.633e-8

5.938e-5

0.0001

4579657

661483338308067761

59.198

72219746840
2³ × 5 × 41 × 397 × 110923

2015-11-03

397

110923

0.0308

0.0012

0.0022

4579657

944538983353845268839577

79.644

103123332528379884
2² × 3⁴ × 7 × 1039 × 43762118867

2019-02-08

1039

43762118867

39,372

455.20

850.18

exponent	prime factors	composite factor	digits	bits*
4579657	27477943 619792459753	17030621880922728079	20	63.885
4579657	27477943 661483338308067761	18176201465478802376895623	26	83.910
4579657	619792459753 661483338308067761	409982385335583170874789323033	30	98.371
4579657	27477943 944538983353845268839577	25953988345874909127993572950111	32	104.356
4579657	619792459753 944538983353845268839577	585418139825477680745042992786044481	36	118.817
4579657	27477943 619792459753 661483338308067761	11265472615255190241056721155309361119	38	123.083
4579657	661483338308067761 944538983353845268839577	624796799871010013346546163179877554577097	42	138.842
4579657	27477943 619792459753 944538983353845268839577	16086086277290505659284488888324341444382583	44	143.529
4579657	27477943 661483338308067761 944538983353845268839577	17168130853438020499165634718725374191648860471471	50	163.554
4579657	619792459753 661483338308067761 944538983353845268839577	38724434543785616928854920568422082974469345330807 7041	54	178.015
4579657	27477943 619792459753 661483338308067761 944538983353845268839577	10640678051013721861909105626486295959137391262472 502372206663	62	202.727

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-07T23:42:00	Will Edgington	Manual testing	?	?	619792459753	39.173	12	1.03428e-8	1.293	2.21718e-8
2015-11-03T12:10:04	TJAOI	Manual testing	2⁵⁹	2⁶⁰*	661483338308067761	59.198	18	0.014	1.259	0.029

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.392 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:	0.392 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	944538983353845268839577	2	0.392

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-02-09T01:18:49	ATH	ec2-ECMCF	50000	5000000	944538983353845268839577	79.644	2	2	8188667380757046	2	0.392

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-17T22:10:23

kkmrkkblmbrbk

c4.xlarge

27477943

619792459753

661483338308067761

CFD7DDFA15A7DD__

2018-02-24T23:21:40

Oliver Kruse

GTX-1

27477943

619792459753

661483338308067761

CFD7DDFA15A7DD__

2019-02-10T00:14:50

EthanD

LexxBuntu

27477943

619792459753

661483338308067761

944538983353845268839577

CFD7DDFA15A7DD82

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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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