M1557607 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	19.0766	68.6567%	500000	15000000	0.0835	4.9710%	19.1602	70.2148%	1.5581%
PrimeNet	2⁵⁷	0.0123	63.1579%	6500	110000	0.0008	2.4228%	0.0131	64.0505%	0.8926%
GPU72	2⁶¹	0.1972	65.5738%	6500	60000	0.0006	1.0501%	0.1978	65.9353%	0.3615%
Difference	+6	+18.8794	+3.0829%	+493500	+14940000	+0.0829	+3.9209%	+18.9624	+4.2795%	+4.2795%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

19.0766

68.6567%

500000

15000000

0.0835

4.9710%

19.1602

70.2148%

1.5581%

PrimeNet

2⁵⁷

0.0123

63.1579%

6500

110000

0.0008

2.4228%

0.0131

64.0505%

0.8926%

GPU72

2⁶¹

0.1972

65.5738%

6500

60000

0.0006

1.0501%

0.1978

65.9353%

0.3615%

Difference

+18.8794

+3.0829%

+493500

+14940000

+0.0829

+3.9209%

+18.9624

+4.2795%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1557607	961532607599	12	39.807	308657 257 × 1201	-	257	1201	8.505e-8	1.998e-5	3.388e-5
1557607	141813590882506426423	21	66.943	45522904969773 3³ × 7 × 11 × 281 × 77923627	2017-12-02	281	77923627	10.921	0.2750	0.5136
1557607	1652984481205331861617	22	70.486	530616670702344 2³ × 3³ × 17 × 2137 × 67619771	2019-07-19	2137	67619771	247.91	0.2387	0.4457

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1557607

961532607599

39.807

308657
257 × 1201

257

1201

8.505e-8

1.998e-5

3.388e-5

1557607

141813590882506426423

66.943

45522904969773
3³ × 7 × 11 × 281 × 77923627

2017-12-02

281

77923627

10.921

0.2750

0.5136

1557607

1652984481205331861617

70.486

530616670702344
2³ × 3³ × 17 × 2137 × 67619771

2019-07-19

2137

67619771

247.91

0.2387

0.4457

exponent	prime factors	composite factor	digits	bits*
1557607	961532607599 141813590882506426423	136358391834234175831382224188377	33	106.749
1557607	961532607599 1652984481205331861617	1589398478534042951442751030627583	34	110.292
1557607	141813590882506426423 1652984481205331861617	234415664952785065878484003919400628305991	42	137.428
1557607	961532607599 141813590882506426423 1652984481205331861617	22539830558410493961152372395763142236021849630382 5609	54	177.235

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:16:17	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 961532607599	-	-	0.084	-	-	4.971%

ECM factoring results:

Old Calculation Method

Total ECM effort:	31.265 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	31.265 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.654	0.000%
25	50000	1.674	18.740%
30	250000	0.144	86.623%
35	1000000	0.010	99.005%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		209	11.69
50000	5000000	141813590882506426423	3	0.168
50000	5000000	1652984481205331861617	39	2.181
250000	40000000		50	17.23

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-02T17:50:16	ATH	ec2-1xe	50000	5000000	141813590882506426423	66.943	3	2		3	0.168
2018-11-12T09:44:10	rucio		50000	5000000						3	0.168
2019-07-19T09:18:03	TJAOI	Manual testing	50000	5000000	1652984481205331861617	70.486	39	2		39	2.181
2019-07-19T09:18:03	TJAOI	Manual testing	50000	5000000						206	11.52
2022-06-16T11:18:31	TJAOI	Manual testing	250000	40000000						50	17.23

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T19:50:56

Oliver Kruse

GTX-2

961532607599

BDDBA4E6984DC3__

2017-10-30T21:47:05

kkmrkkblmbrbk

c4.xlarge

961532607599

BDDBA4E6984DC3__

2017-12-03T09:47:00

kkmrkkblmbrbk

c4.xlarge

961532607599

141813590882506426423

DD85B4871F8446__

2017-12-03T10:04:34

ATH

ec2-1xf

961532607599

141813590882506426423

DD85B4871F8446__

2019-07-19T14:33:55

ATH

ec2-PRPCF

961532607599

141813590882506426423

1652984481205331861617

DD85B4871F844640

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

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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