M1692959 Mersenne number exponent details

Residue

Status

L-L

09DC02B7C4CAAD2E

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	17.5515	68.6567%	500000	15000000	0.0880	5.0212%	17.6395	70.2305%	1.5738%
PrimeNet	2⁵⁷	0.0113	63.1579%	8000	130000	0.0010	2.7291%	0.0123	64.1634%	1.0055%
GPU72	2⁶¹	0.1814	65.5738%	7000	100000	0.0008	1.3001%	0.1823	66.0214%	0.4476%
Difference	+6	+17.3700	+3.0829%	+493000	+14900000	+0.0872	+3.7211%	+17.4572	+4.2092%	+4.2092%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.5515

68.6567%

500000

15000000

0.0880

5.0212%

17.6395

70.2305%

1.5738%

PrimeNet

2⁵⁷

0.0113

63.1579%

8000

130000

0.0010

2.7291%

0.0123

64.1634%

1.0055%

GPU72

2⁶¹

0.1814

65.5738%

7000

100000

0.0008

1.3001%

0.1823

66.0214%

0.4476%

Difference

+17.3700

+3.0829%

+493000

+14900000

+0.0872

+3.7211%

+17.4572

+4.2092%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1692959	37175966817779503583449	23	74.977	10979582735842836 2² × 3 × 59 × 131 × 118380803207	2009-06-14	131	118380803207	2,805.8	440.13	822.04

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1692959

37175966817779503583449

74.977

10979582735842836
2² × 3 × 59 × 131 × 118380803207

2009-06-14

131

118380803207

2,805.8

440.13

822.04

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-17T19:18:49	alpertron	Manual testing	500000	15000000	12	-		-	-	0.088	-	-	5.021%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-17T19:18:49

alpertron

Manual testing

500000

15000000

0.088

-

-

5.021%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.023	-	-
2003-03-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.023	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.685 GHz-days
Estimated T-Level:	24.714

Digits	B1	Curves	Complete	FacMiss
20	11000	264 / 100	2.640	7.042%
25	50000	264 / 280	0.943	38.886%

New Calculation Method

Total ECM effort:	15.685 GHz-days
Estimated T-Level:	24.714

Digits	B1	Complete	FacMiss
20	11000	10.154	0.004%
25	50000	0.940	39.082%
30	250000	0.059	94.246%
35	1000000	0.003	99.723%

ECM Summary

B1	B2	factor	curves	GHz-days
		37175966817779503583449	1	0.00000e+0
50000	5000000		264	15.69

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-06-22T09:00:00	Scott Kurowski	UW2	50000	5000000						3	0.178
2009-06-14T18:36:00	KAMCOBILL	PC01			37175966817779503583449	74.977		1		1	-
2020-01-25T16:47:19	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-01-31T16:34:03	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-07T18:57:25	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-15T23:57:04	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-23T22:19:45	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-02-24T10:24:12	TJAOI	Manual testing	50000	5000000						246	14.62

date	userid	compid	res64	spent (GHz-days)
1998-11-21T00:00:00	Morgan Savage	v4_computers	09DC02B7C4CAAD2E	0.080

date

userid

compid

res64

spent (GHz-days)

1998-11-21T00:00:00

Morgan Savage

v4_computers

09DC02B7C4CAAD2E

0.080

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)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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