M1557593 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	19.0768	68.6567%	500000	15000000	0.0835	4.9710%	19.1604	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	+18.8796	+3.0829%	+493500	+14940000	+0.0829	+3.9209%	+18.9625	+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

19.0768

68.6567%

500000

15000000

0.0835

4.9710%

19.1604

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

+18.8796

+3.0829%

+493500

+14940000

+0.0829

+3.9209%

+18.9625

+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
1557593	9345559	7	23.156	3 3	-	1	3	7.179e-13	7.182e-8	1.318e-7
1557593	86267878852263067357841	23	76.191	27692689570466440 2³ × 5 × 13 × 31 × 1717908782287	2017-12-02	31	1717908782287	10,931	6,061.9	11,322

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1557593

9345559

23.156

3
3

7.179e-13

7.182e-8

1.318e-7

1557593

86267878852263067357841

76.191

27692689570466440
2³ × 5 × 13 × 31 × 1717908782287

2017-12-02

1717908782287

10,931

6,061.9

11,322

exponent	prime factors	composite factor	digits	bits*
1557593	9345559 86267878852263067357841	806221551618676779513677178119	30	99.347

exponent

prime factors

composite factor

digits

bits*

1557593

9345559
86267878852263067357841

806221551618676779513677178119

99.347

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: 9345559	-	-	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		248	13.87
50000	5000000	86267878852263067357841	3	0.168
250000	40000000		50	17.23

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-02T17:49:26	ATH	ec2-1xe	50000	5000000	86267878852263067357841	76.191	3	2		3	0.168
2018-11-12T09:45:51	rucio		50000	5000000						3	0.168
2019-07-19T09:18:03	TJAOI	Manual testing	50000	5000000						245	13.70
2022-06-16T11:18:30	TJAOI	Manual testing	250000	40000000						50	17.23

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T19:52:32

Oliver Kruse

GTX-1

9345559

880972B2D060FC__

2017-10-30T21:40:12

kkmrkkblmbrbk

c4.xlarge

9345559

880972B2D060FC__

2017-12-03T09:54:34

kkmrkkblmbrbk

c4.xlarge

9345559

86267878852263067357841

70E59C0C81508A__

2017-12-04T04:27:43

Oliver Kruse

GTX-1

9345559

86267878852263067357841

70E59C0C81508A__

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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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