M1659817 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	17.9019	68.6567%	500000	15000000	0.0880	5.0093%	17.9900	70.2268%	1.5701%
PrimeNet	2⁵⁷	0.0116	63.1579%	7000	120000	0.0009	2.5664%	0.0125	64.1034%	0.9455%
GPU72	2⁶¹	0.1851	65.5738%	7000	70000	0.0007	1.1526%	0.1858	65.9706%	0.3968%
Difference	+6	+17.7169	+3.0829%	+493000	+14930000	+0.0873	+3.8567%	+17.8042	+4.2562%	+4.2562%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.9019

68.6567%

500000

15000000

0.0880

5.0093%

17.9900

70.2268%

1.5701%

PrimeNet

2⁵⁷

0.0116

63.1579%

7000

120000

0.0009

2.5664%

0.0125

64.1034%

0.9455%

GPU72

2⁶¹

0.1851

65.5738%

7000

70000

0.0007

1.1526%

0.1858

65.9706%

0.3968%

Difference

+17.7169

+3.0829%

+493000

+14930000

+0.0873

+3.8567%

+17.8042

+4.2562%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1659817	9354343534457	13	43.089	2817884 2² × 659 × 1069	-	659	1069	1.364e-6	4.649e-5	9.152e-5
1659817	125061293277481849	18	56.795	37673217372 2² × 3 × 7 × 59 × 131 × 58027	2015-04-20	131	58027	0.0061	0.0002	0.0004
1659817	315550820871329674303	21	68.096	95055907028103 3³ × 7 × 23 × 41 × 533341789	2018-01-14	41	533341789	39.676	1.9829	3.7036

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1659817

9354343534457

43.089

2817884
2² × 659 × 1069

659

1069

1.364e-6

4.649e-5

9.152e-5

1659817

125061293277481849

56.795

37673217372
2² × 3 × 7 × 59 × 131 × 58027

2015-04-20

131

58027

0.0061

0.0002

0.0004

1659817

315550820871329674303

68.096

95055907028103
3³ × 7 × 23 × 41 × 533341789

2018-01-14

533341789

39.676

1.9829

3.7036

exponent	prime factors	composite factor	digits	bits*
1659817	9354343534457 125061293277481849	1169866300181043013023323570993	31	99.884
1659817	9354343534457 315550820871329674303	2951770781010321709936791667958471	34	111.185
1659817	125061293277481849 315550820871329674303	39463193752939500926446402893164226247	38	124.892
1659817	9354343534457 125061293277481849 315550820871329674303	36915227133183349352958427042461567871591358829287 9	51	167.981

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2015-04-20T21:08:00	alpertron	Manual testing	500000	15000000	12		125061293277481849	18	56.795	0.034	0.156	0.068	5.009%

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.882 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	14.882 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		248	14.70
50000	5000000	315550820871329674303	3	0.178

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-05-27T11:35:00	Richard B. Woods	Puttputt	50000	5000000						1	0.059
2018-01-15T03:07:58	Chang Chia-Tche	exbpc13	50000	5000000	315550820871329674303	68.096	3	2		3	0.178
2019-02-10T11:55:45	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2019-12-16T13:26:56	TJAOI	Manual testing	50000	5000000						244	14.47

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-02T20:32:46

Oliver Kruse

GTX-2

9354343534457

125061293277481849

7F038A73B36C51__

2017-11-02T17:34:44

kkmrkkblmbrbk

c4.xlarge

9354343534457

125061293277481849

7F038A73B36C51__

2018-01-15T03:24:52

ATH

ec2-8x

9354343534457

125061293277481849

315550820871329674303

26D2FFDBA5D364__

2018-01-15T15:44:00

kkmrkkblmbrbk

c4.xlarge

9354343534457

125061293277481849

315550820871329674303

26D2FFDBA5D364__

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

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