M1697287 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	17.5067	68.6567%	500000	15000000	0.0880	5.0228%	17.5947	70.2310%	1.5743%
PrimeNet	2⁵⁷	0.0113	63.1579%	8000	130000	0.0010	2.7305%	0.0123	64.1639%	1.0060%
GPU72	2⁶¹	0.1810	65.5738%	7000	100000	0.0008	1.3009%	0.1818	66.0216%	0.4478%
Difference	+6	+17.3257	+3.0829%	+493000	+14900000	+0.0872	+3.7219%	+17.4129	+4.2094%	+4.2094%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.5067

68.6567%

500000

15000000

0.0880

5.0228%

17.5947

70.2310%

1.5743%

PrimeNet

2⁵⁷

0.0113

63.1579%

8000

130000

0.0010

2.7305%

0.0123

64.1639%

1.0060%

GPU72

2⁶¹

0.1810

65.5738%

7000

100000

0.0008

1.3009%

0.1818

66.0216%

0.4478%

Difference

+17.3257

+3.0829%

+493000

+14900000

+0.0872

+3.7219%

+17.4129

+4.2094%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1697287	27156593	8	24.695	8 2³	-	8	8	1.319e-12	5.459e-7	1.111e-6
1697287	694328020603401094129	21	69.234	204540546355272 2³ × 3⁴ × 10253 × 30786013	2018-07-24	10253	30786013	101.63	0.1151	0.2138
1697287	964133099701218823433	21	69.708	284021824152668 2² × 7 × 662443 × 15312467	2018-03-05	662443	15312467	100.65	0.0997	0.1063

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1697287

27156593

24.695

8
2³

1.319e-12

5.459e-7

1.111e-6

1697287

694328020603401094129

69.234

204540546355272
2³ × 3⁴ × 10253 × 30786013

2018-07-24

10253

30786013

101.63

0.1151

0.2138

1697287

964133099701218823433

69.708

284021824152668
2² × 7 × 662443 × 15312467

2018-03-05

662443

15312467

100.65

0.0997

0.1063

exponent	prime factors	composite factor	digits	bits*
1697287	27156593 694328020603401094129	18855583464022177929015942497	29	93.929
1697287	27156593 964133099701218823433	26182570186414421191908843769	29	94.403
1697287	694328020603401094129 964133099701218823433	669424626713768824506664173714322263924857	42	138.942
1697287	27156593 694328020603401094129 964133099701218823433	18179292131842747463215904753241147992245924132201	50	163.637

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-17T19:18:52	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 27156593	-	-	0.088	-	-	5.023%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-17T19:18:52

alpertron

Manual testing

500000

15000000

skipped known factor: 27156593

0.088

-

-

5.023%

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.630 GHz-days
Estimated T-Level:	24.696

Digits	B1	Curves	Complete	FacMiss
20	11000	263 / 100	2.630	7.113%
25	50000	263 / 280	0.939	39.025%

New Calculation Method

Total ECM effort:	15.630 GHz-days
Estimated T-Level:	24.696

Digits	B1	Complete	FacMiss
20	11000	8.484	0.021%
25	50000	0.767	46.451%
30	250000	0.047	95.388%
35	1000000	0.002	99.784%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		261	15.51
50000	5000000	694328020603401094129	1	0.059
50000	5000000	964133099701218823433	1	0.059

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-01-19T16:49:35	Richard B. Woods	Puttputt	50000	5000000						1	0.059
2018-03-05T05:34:10	Oliver Kruse	ECM-HTC	50000	5000000	964133099701218823433	69.708	1	2		1	0.059
2018-07-24T05:39:45	Chang Chia-Tche	exbpc13	50000	5000000	694328020603401094129	69.234	1	2		1	0.059
2018-11-24T06:02:19	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2020-01-29T02:25:15	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-04T18:36:17	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-12T10:17:53	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-20T10:28:22	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-24T10:24:30	TJAOI	Manual testing	50000	5000000						245	14.56

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:16:36

alpertron

Manual testing

27156593

49FBB42A23E271__

2017-10-18T16:08:11

Oliver Kruse

Threadripper

27156593

49FBB42A23E271__

2018-03-09T15:57:32

trebor

Desktop

27156593

964133099701218823433

55782DB40B211F__

2018-03-10T02:04:57

ANONYMOUS

dory

27156593

964133099701218823433

55782DB40B211F__

2018-03-11T06:10:16

Chang Chia-Tche

exbpc13

27156593

964133099701218823433

55782DB40B211F__

2018-07-24T11:22:31

_p95holder_

b_PRPt11_TFL7

27156593

694328020603401094129

964133099701218823433

55782DB40B211F__

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

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