M1792073 Mersenne number exponent details

Residue

Status

L-L

D5058B6F80D10119

double-checked

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	16.5808	68.6567%	500000	15000000	0.1015	5.0558%	16.6822	70.2414%	1.5847%
PrimeNet	2⁵⁷	0.0107	63.1579%	8000	140000	0.0012	2.8151%	0.0119	64.1950%	1.0371%
GPU72	2⁶¹	0.1714	65.5738%	8000	130000	0.0012	1.4937%	0.1726	66.0880%	0.5142%
Difference	+6	+16.4093	+3.0829%	+492000	+14870000	+0.1003	+3.5621%	+16.5097	+4.1534%	+4.1534%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.5808

68.6567%

500000

15000000

0.1015

5.0558%

16.6822

70.2414%

1.5847%

PrimeNet

2⁵⁷

0.0107

63.1579%

8000

140000

0.0012

2.8151%

0.0119

64.1950%

1.0371%

GPU72

2⁶¹

0.1714

65.5738%

8000

130000

0.0012

1.4937%

0.1726

66.0880%

0.5142%

Difference

+16.4093

+3.0829%

+492000

+14870000

+0.1003

+3.5621%

+16.5097

+4.1534%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1792073	4113683074471518617	19	61.835	1147744281196 2² × 37 × 41 × 189147047	2016-06-03	41	189147047	0.1876	0.8106	1.5140
1792073	3665377109205213303257	22	71.634	1022664006769036 2² × 29 × 8816069023871	2009-07-11	29	8816069023871	267.70	37,783	70,569

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1792073

4113683074471518617

61.835

1147744281196
2² × 37 × 41 × 189147047

2016-06-03

189147047

0.1876

0.8106

1.5140

1792073

3665377109205213303257

71.634

1022664006769036
2² × 29 × 8816069023871

2009-07-11

8816069023871

267.70

37,783

70,569

exponent	prime factors	composite factor	digits	bits*
1792073	4113683074471518617 3665377109205213303257	15078199775692829103483850117959742235569	41	133.470

exponent

prime factors

composite factor

digits

bits*

1792073

4113683074471518617
3665377109205213303257

15078199775692829103483850117959742235569

133.470

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:34:44	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.056%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:34:44

alpertron

Manual testing

500000

15000000

0.101

-

-

5.056%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-
2022-03-08T23:06:27	LordJulius	Manual testing	2⁵⁸	2⁶¹		-	-	0.150	-	-
2022-03-09T03:44:01	LordJulius	Manual testing	2¹	2⁶¹		-	-	0.171	-	-
2016-06-03T15:39:50	TJAOI	Manual testing	2⁶¹	2⁶²*	4113683074471518617	61.835	19	0.016	0.197	0.033

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.709 GHz-days
Estimated T-Level:	24.589

Digits	B1	Curves	Complete	FacMiss
20	11000	257 / 100	2.570	7.555%
25	50000	257 / 280	0.918	39.872%

New Calculation Method

Total ECM effort:	17.709 GHz-days
Estimated T-Level:	24.589

Digits	B1	Complete	FacMiss
20	11000	9.885	0.005%
25	50000	0.915	40.068%
30	250000	0.058	94.394%
35	1000000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
		3665377109205213303257	1	0.00000e+0
50000	5000000		257	17.71

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-09-04T19:37:00	Scott Kurowski	HomeOffice	50000	5000000						3	0.207
2009-07-11T06:56:00	SubPrime	stor			3665377109205213303257	71.634		1		1	-
2015-03-06T15:42:00	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2020-03-11T15:04:50	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.207
2020-03-31T07:17:15	Hans Loeblich	crow	50000	5000000						3	0.207
2020-05-01T22:11:46	Oliver Kruse	Melissa	50000	5000000						3	0.207
2020-05-27T11:53:45	nordi	sweet16	50000	5000000						3	0.207
2020-06-27T01:26:39	nordi	sweet16	50000	5000000						3	0.207
2020-07-24T15:38:13	Ahmed Azhad	c5.large.az	50000	5000000						3	0.207
2020-09-29T07:54:27	nordi	sweet16	50000	5000000						7	0.482
2020-11-20T10:38:05	TJAOI	Manual testing	50000	5000000						228	15.71

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	D5058B6F80D10119	0.097

date

userid

compid

res64

spent (GHz-days)

1998-12-21T00:00:00

ANONYMOUS

v4_computers

D5058B6F80D10119

0.097

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T16:40:25

Oliver Kruse

GTX-0

4113683074471518617

3665377109205213303257

5A9A0C26AE6C57C0

2017-10-05T21:07:13

Oliver Kruse

Manual testing

4113683074471518617

3665377109205213303257

5A9A0C26AE6C57__

2017-11-11T02:50:55

kkmrkkblmbrbk

c4.xlarge

4113683074471518617

3665377109205213303257

5A9A0C26AE6C57__

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

10¹³

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