M1794587 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	16.5575	68.6567%	500000	15000000	0.1015	5.0567%	16.6590	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	+16.3864	+3.0829%	+492000	+14870000	+0.1003	+3.5625%	+16.4867	+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

16.5575

68.6567%

500000

15000000

0.1015

5.0567%

16.6590

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

+16.3864

+3.0829%

+492000

+14870000

+0.1003

+3.5625%

+16.4867

+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
1794587	27467948623	11	34.677	7653 3 × 2551	-	3	2551	2.113e-9	1.116e-5	2.045e-5
1794587	195011315211363317645519	24	77.368	54333201792769957 43 × 109 × 11592319563211	2018-12-21	109	11592319563211	22,952	49,682	92,792

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1794587

27467948623

34.677

7653
3 × 2551

2551

2.113e-9

1.116e-5

2.045e-5

1794587

195011315211363317645519

77.368

54333201792769957
43 × 109 × 11592319563211

2018-12-21

109

11592319563211

22,952

49,682

92,792

exponent	prime factors	composite factor	digits	bits*
1794587	27467948623 195011315211363317645519	5356560787129385994873945218170337	34	112.045

exponent

prime factors

composite factor

digits

bits*

1794587

27467948623
195011315211363317645519

5356560787129385994873945218170337

112.045

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:35:00	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 27467948623	-	-	0.101	-	-	5.057%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:35:00

alpertron

Manual testing

500000

15000000

skipped known factor: 27467948623

0.101

-

-

5.057%

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.263 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:	18.263 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		263	18.13
50000	5000000	195011315211363317645519	2	0.138

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-14T22:53:57	alpertron	laptop2	50000	5000000						3	0.207
2018-12-21T05:40:37	Chang Chia-Tche	exbpc13	50000	5000000	195011315211363317645519	77.368	2	2		2	0.138
2020-03-13T12:56:47	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.207
2020-04-09T20:34:08	Oliver Kruse	Melissa	50000	5000000						3	0.207
2020-05-02T23:49:04	Greg Hogan	azure2	50000	5000000						3	0.207
2020-06-01T15:07:02	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-06-29T12:56:45	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.207
2020-07-26T04:30:33	Ahmed Azhad	c5.4xlarge.azf	50000	5000000						3	0.207
2020-10-05T03:42:08	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.482
2020-12-01T13:44:32	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.482
2021-01-01T10:30:09	TJAOI	Manual testing	50000	5000000						228	15.71

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T17:10:22

Oliver Kruse

GTX-3

27467948623

FA539EBA610AC0__

2017-11-05T21:46:14

bayanne

iMac1

27467948623

FA539EBA610AC0__

2018-12-21T05:53:14

ATH

ec2-PRPCF

27467948623

195011315211363317645519

822D56A9388B34A5

2018-12-22T01:23:47

kkmrkkblmbrbk

c5.large

27467948623

195011315211363317645519

822D56A9388B34A5

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

10¹⁴

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