M1732811 Mersenne number exponent details

Residue

Status

L-L

687C471D9D509276

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	17.1478	68.6567%	500000	15000000	0.1015	5.0353%	17.2493	70.2350%	1.5782%
PrimeNet	2⁵⁷	0.0111	63.1579%	8000	140000	0.0012	2.7972%	0.0123	64.1885%	1.0306%
GPU72	2⁶¹	0.1773	65.5738%	7000	110000	0.0010	1.3458%	0.1783	66.0371%	0.4633%
Difference	+6	+16.9705	+3.0829%	+493000	+14890000	+0.1005	+3.6895%	+17.0710	+4.1979%	+4.1979%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.1478

68.6567%

500000

15000000

0.1015

5.0353%

17.2493

70.2350%

1.5782%

PrimeNet

2⁵⁷

0.0111

63.1579%

8000

140000

0.0012

2.7972%

0.0123

64.1885%

1.0306%

GPU72

2⁶¹

0.1773

65.5738%

7000

110000

0.0010

1.3458%

0.1783

66.0371%

0.4633%

Difference

+16.9705

+3.0829%

+493000

+14890000

+0.1005

+3.6895%

+17.0710

+4.1979%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1732811	112019700268515929	18	56.637	32323115524 2² × 7 × 22369 × 51607	1998-11-21	22369	51607	0.0075	0.0019	0.0036

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1732811

112019700268515929

56.637

32323115524
2² × 7 × 22369 × 51607

1998-11-21

22369

51607

0.0075

0.0019

0.0036

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:33:18	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 112019700268515929	-	-	0.101	-	-	5.035%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:33:18

alpertron

Manual testing

500000

15000000

skipped known factor: 112019700268515929

0.101

-

-

5.035%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
1998-11-21T00:00:00	ANONYMOUS	v4_computers	?	?	112019700268515929	56.637	18	0.002	0.191	0.004

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

1998-11-21T00:00:00

ANONYMOUS

v4_computers

112019700268515929

56.637

0.002

0.191

0.004

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.645 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:	17.645 GHz-days
Estimated T-Level:	24.589

Digits	B1	Complete	FacMiss
20	11000	8.290	0.025%
25	50000	0.749	47.271%
30	250000	0.046	95.491%
35	1000000	0.002	99.789%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		257	17.64

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-11-28T20:49:41	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-15T00:42:41	Gordon Spence	haswell	50000	5000000						3	0.206
2019-06-17T19:54:52	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2020-02-15T21:41:35	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-02-23T19:37:04	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-03T10:35:03	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-15T19:14:23	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-04-12T17:10:12	Oliver Kruse	IOS-2	50000	5000000						3	0.206
2020-05-04T17:55:02	Greg Hogan	azure2	50000	5000000						3	0.206
2020-05-25T09:38:33	TJAOI	Manual testing	50000	5000000						232	15.93

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)

10³

10⁴

10⁵

10⁶

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