M1782167 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	16.6729	68.6567%	500000	15000000	0.1015	5.0524%	16.7744	70.2403%	1.5836%
PrimeNet	2⁵⁷	0.0108	63.1579%	8000	140000	0.0012	2.8122%	0.0120	64.1940%	1.0361%
GPU72	2⁶¹	0.1724	65.5738%	8000	130000	0.0012	1.4920%	0.1735	66.0874%	0.5136%
Difference	+6	+16.5006	+3.0829%	+492000	+14870000	+0.1003	+3.5604%	+16.6009	+4.1529%	+4.1529%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.6729

68.6567%

500000

15000000

0.1015

5.0524%

16.7744

70.2403%

1.5836%

PrimeNet

2⁵⁷

0.0108

63.1579%

8000

140000

0.0012

2.8122%

0.0120

64.1940%

1.0361%

GPU72

2⁶¹

0.1724

65.5738%

8000

130000

0.0012

1.4920%

0.1735

66.0874%

0.5136%

Difference

+16.5006

+3.0829%

+492000

+14870000

+0.1003

+3.5604%

+16.6009

+4.1529%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1782167	352954610017	12	38.361	99024 2⁴ × 3 × 2063	-	16	2063	2.946e-8	1.003e-5	1.650e-5
1782167	129957646671904315169887	24	76.782	36460569259756329 3 × 137 × 5159159 × 17195021	2020-07-19	5159159	17195021	11,727	0.4574	0.8259

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1782167

352954610017

38.361

99024
2⁴ × 3 × 2063

2063

2.946e-8

1.003e-5

1.650e-5

1782167

129957646671904315169887

76.782

36460569259756329
3 × 137 × 5159159 × 17195021

2020-07-19

5159159

17195021

11,727

0.4574

0.8259

exponent	prime factors	composite factor	digits	bits*
1782167	352954610017 129957646671904315169887	45869150499809065511526923186958079	35	115.143

exponent

prime factors

composite factor

digits

bits*

1782167

352954610017
129957646671904315169887

45869150499809065511526923186958079

115.143

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:33:26	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 352954610017	-	-	0.101	-	-	5.052%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:33:26

alpertron

Manual testing

500000

15000000

skipped known factor: 352954610017

0.101

-

-

5.052%

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.767 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	17.767 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.323	0.024%
25	50000	0.752	47.133%
30	250000	0.046	95.474%
35	1000000	0.002	99.788%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		256	17.63
50000	5000000	129957646671904315169887	2	0.138

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-13T01:01:44	alpertron	laptop2	50000	5000000						3	0.207
2018-12-02T01:37:36	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-03-08T16:36:58	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.207
2020-03-21T21:09:28	Hans Loeblich	tomservo	50000	5000000						3	0.207
2020-04-29T15:22:39	Greg	azure2	50000	5000000						3	0.207
2020-05-17T02:55:14	alpertron	laptop3	50000	5000000						3	0.207
2020-06-22T07:02:58	MarkS	desktop-i7	50000	5000000						3	0.207
2020-07-19T19:16:15	nordi	sweet16	50000	5000000	129957646671904315169887	76.782	2	2	7046002340758157	2	0.138
2020-08-10T14:49:59	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						3	0.207
2020-10-14T19:38:19	nordi	sweet16	50000	5000000						7	0.482
2020-11-13T10:46:23	TJAOI	Manual testing	50000	5000000						225	15.49

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T14:25:49

Oliver Kruse

GTX-3

352954610017

AC70106F7F8A70__

2017-11-04T18:13:28

ATH

ec2-1xf

352954610017

AC70106F7F8A70__

2020-07-22T07:34:12

Sébastien Broucke

Portable_Seb

352954610017

129957646671904315169887

9ABA258421995980

2020-07-22T09:50:47

Bommer

6600K

352954610017

129957646671904315169887

9ABA258421995980

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

10⁷

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