M1794659 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	16.5569	68.6567%	500000	15000000	0.1015	5.0567%	16.6583	70.2416%	1.5849%
PrimeNet	2⁵⁷	0.0107	63.1579%	8000	140000	0.0012	2.8159%	0.0119	64.1953%	1.0374%
GPU72	2⁶¹	0.1712	65.5738%	8000	130000	0.0012	1.4942%	0.1723	66.0882%	0.5144%
Difference	+6	+16.3857	+3.0829%	+492000	+14870000	+0.1003	+3.5625%	+16.4860	+4.1535%	+4.1535%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.5569

68.6567%

500000

15000000

0.1015

5.0567%

16.6583

70.2416%

1.5849%

PrimeNet

2⁵⁷

0.0107

63.1579%

8000

140000

0.0012

2.8159%

0.0119

64.1953%

1.0374%

GPU72

2⁶¹

0.1712

65.5738%

8000

130000

0.0012

1.4942%

0.1723

66.0882%

0.5144%

Difference

+16.3857

+3.0829%

+492000

+14870000

+0.1003

+3.5625%

+16.4860

+4.1535%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1794659	86143633	8	26.360	24 2³ × 3	-	8	8	5.007e-12	6.293e-7	1.281e-6
1794659	4445517638735931891121	22	71.913	1238541037248840 2³ × 3 × 5 × 13 × 281 × 2825397019	2020-05-07	281	2825397019	529.42	12.109	22.616

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1794659

86143633

26.360

24
2³ × 3

5.007e-12

6.293e-7

1.281e-6

1794659

4445517638735931891121

71.913

1238541037248840
2³ × 3 × 5 × 13 × 281 × 2825397019

2020-05-07

281

2825397019

529.42

12.109

22.616

exponent	prime factors	composite factor	digits	bits*
1794659	86143633 4445517638735931891121	382953039966294700741723382593	30	98.273

exponent

prime factors

composite factor

digits

bits*

1794659

86143633
4445517638735931891121

382953039966294700741723382593

98.273

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:35:02	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 86143633	-	-	0.101	-	-	5.057%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:35:02

alpertron

Manual testing

500000

15000000

skipped known factor: 86143633

0.101

-

-

5.057%

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.264 GHz-days
Estimated T-Level:	24.732

Digits	B1	Curves	Complete	FacMiss
20	11000	265 / 100	2.650	6.972%
25	50000	265 / 280	0.946	38.747%

New Calculation Method

Total ECM effort:	18.264 GHz-days
Estimated T-Level:	24.732

Digits	B1	Complete	FacMiss
20	11000	8.548	0.019%
25	50000	0.773	46.181%
30	250000	0.048	95.354%
35	1000000	0.002	99.782%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		264	18.19
50000	5000000	4445517638735931891121	1	0.069

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-14T10:56:08	ATH	ec2-1xe	50000	5000000						3	0.207
2018-12-21T10:01:31	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-03-17T18:38:41	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.207
2020-04-17T19:16:18	Oliver Kruse	IOS-2	50000	5000000						3	0.207
2020-05-07T13:51:29	Chang Chia-Tche	exbpc13	50000	5000000	4445517638735931891121	71.913	1	2		1	0.069
2020-05-18T21:43:28	kracker	O0	50000	5000000						3	0.207
2020-06-23T02:20:15	nordi	sweet16	50000	5000000						3	0.207
2020-07-20T00:55:03	MarkS	desktop-i7	50000	5000000						3	0.207
2020-09-18T10:56:58	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						7	0.482
2020-11-23T11:59:42	nordi	sweet16	50000	5000000						7	0.482
2021-01-08T11:39:47	TJAOI	Manual testing	50000	5000000						229	15.78

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T17:11:48

Oliver Kruse

GTX-2

86143633

36BA14D07FF748__

2017-11-05T22:43:55

bayanne

iMac1

86143633

36BA14D07FF748__

2020-05-08T11:41:08

mnd9

mnd

86143633

4445517638735931891121

C25D424E9C19A204

2020-05-08T12:59:08

Klaus Nordmann

no1

86143633

4445517638735931891121

C25D424E9C19A204

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

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