M1759333 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	16.8893	68.6567%	500000	15000000	0.1015	5.0446%	16.9908	70.2379%	1.5811%
PrimeNet	2⁵⁷	0.0109	63.1579%	8000	140000	0.0012	2.8053%	0.0121	64.1914%	1.0335%
GPU72	2⁶¹	0.1746	65.5738%	8000	120000	0.0011	1.4525%	0.1757	66.0738%	0.5001%
Difference	+6	+16.7147	+3.0829%	+492000	+14880000	+0.1004	+3.5920%	+16.8151	+4.1640%	+4.1640%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.8893

68.6567%

500000

15000000

0.1015

5.0446%

16.9908

70.2379%

1.5811%

PrimeNet

2⁵⁷

0.0109

63.1579%

8000

140000

0.0012

2.8053%

0.0121

64.1914%

1.0335%

GPU72

2⁶¹

0.1746

65.5738%

8000

120000

0.0011

1.4525%

0.1757

66.0738%

0.5001%

Difference

+16.7147

+3.0829%

+492000

+14880000

+0.1004

+3.5920%

+16.8151

+4.1640%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1759333	160943782841	12	37.228	45740 2² × 5 × 2287	-	5	2287	1.978e-8	1.017e-5	1.828e-5
1759333	16856529620007402074981167	26	83.802	4790602353280306251 3 × 13 × 347 × 2657 × 133230754471	2020-05-19	2657	133230754471	1,762,002	570.99	1,066.5

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1759333

160943782841

37.228

45740
2² × 5 × 2287

2287

1.978e-8

1.017e-5

1.828e-5

1759333

16856529620007402074981167

83.802

4790602353280306251
3 × 13 × 347 × 2657 × 133230754471

2020-05-19

2657

133230754471

1,762,002

570.99

1,066.5

exponent	prime factors	composite factor	digits	bits*
1759333	160943782841 16856529620007402074981167	2712953642615355568368341740812755447	37	121.029

exponent

prime factors

composite factor

digits

bits*

1759333

160943782841
16856529620007402074981167

2712953642615355568368341740812755447

121.029

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:30:08	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 160943782841	-	-	0.101	-	-	5.045%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:30:08

alpertron

Manual testing

500000

15000000

skipped known factor: 160943782841

0.101

-

-

5.045%

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.637 GHz-days
Estimated T-Level:	24.839

Digits	B1	Curves	Complete	FacMiss
20	11000	271 / 100	2.710	6.564%
25	50000	271 / 280	0.968	37.924%

New Calculation Method

Total ECM effort:	18.637 GHz-days
Estimated T-Level:	24.839

Digits	B1	Complete	FacMiss
20	11000	8.742	0.016%
25	50000	0.790	45.381%
30	250000	0.049	95.251%
35	1000000	0.002	99.777%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	17.26
50000	5000000	16856529620007402074981167	20	1.375

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-06-04T11:33:10	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-21T06:28:14	Alvin Bunk	WorkCAT	50000	5000000						3	0.206
2019-08-02T14:58:42	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2020-02-27T17:46:15	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-09T06:05:46	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-22T09:01:21	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-04-30T01:48:08	Greg	azure4	50000	5000000						3	0.206
2020-05-19T23:56:24	nordi	sweet16	50000	5000000	16856529620007402074981167	83.802	20	2	2069112390240833	20	1.375
2020-08-28T11:14:35	TJAOI	Manual testing	50000	5000000						232	15.95

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T08:59:02

Oliver Kruse

GTX-3

160943782841

A7F2E09F6D6886__

2017-11-04T05:12:33

Chang Chia-Tche

exbpc13

160943782841

A7F2E09F6D6886__

2020-05-20T02:19:04

CrypticClue

cruncher

160943782841

16856529620007402074981167

14875882B7091C3A

2020-05-21T00:23:53

Luigi Morelli

9800X

160943782841

16856529620007402074981167

14875882B7091C3A

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

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