M1718593 Mersenne number exponent details

Residue

Status

L-L

D118CBB16FDC17A0

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	17.2897	68.6567%	500000	15000000	0.0880	5.0303%	17.3777	70.2334%	1.5767%
PrimeNet	2⁵⁷	0.0112	63.1579%	8000	140000	0.0010	2.7929%	0.0122	64.1868%	1.0290%
GPU72	2⁶¹	0.1787	65.5738%	7000	110000	0.0009	1.3434%	0.1796	66.0363%	0.4625%
Difference	+6	+17.1109	+3.0829%	+493000	+14890000	+0.0872	+3.6869%	+17.1981	+4.1971%	+4.1971%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.2897

68.6567%

500000

15000000

0.0880

5.0303%

17.3777

70.2334%

1.5767%

PrimeNet

2⁵⁷

0.0112

63.1579%

8000

140000

0.0010

2.7929%

0.0122

64.1868%

1.0290%

GPU72

2⁶¹

0.1787

65.5738%

7000

110000

0.0009

1.3434%

0.1796

66.0363%

0.4625%

Difference

+17.1109

+3.0829%

+493000

+14890000

+0.0872

+3.6869%

+17.1981

+4.1971%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1718593	7694022098758132009	19	62.738	2238465447828 2² × 3² × 43 × 2111 × 685001	2009-09-24	2111	685001	0.7566	0.0027	0.0048

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1718593

7694022098758132009

62.738

2238465447828
2² × 3² × 43 × 2111 × 685001

2009-09-24

2111

685001

0.7566

0.0027

0.0048

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:30:53	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 7694022098758132009	-	-	0.088	-	-	5.030%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2003-02-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2003-02-02T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁸

0.022

-

-

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.889 GHz-days
Estimated T-Level:	24.768

Digits	B1	Curves	Complete	FacMiss
20	11000	267 / 100	2.670	6.833%
25	50000	267 / 280	0.954	38.471%

New Calculation Method

Total ECM effort:	15.889 GHz-days
Estimated T-Level:	24.768

Digits	B1	Complete	FacMiss
20	11000	10.269	0.003%
25	50000	0.950	38.667%
30	250000	0.060	94.183%
35	1000000	0.003	99.720%

ECM Summary

B1	B2	factor	curves	GHz-days
		7694022098758132009	1	0.00000e+0
50000	5000000		267	15.89

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-03T16:52:00	paulie	iMac3.4	50000	5000000						3	0.179
2009-09-24T16:43:00	SubPrime	stor			7694022098758132009	62.738		1		1	-
2020-02-04T03:12:23	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.179
2020-02-11T16:20:44	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.179
2020-02-19T20:51:00	-Anonymous-	aws-nano	50000	5000000						3	0.179
2020-02-27T18:30:23	kracker	O0	50000	5000000						3	0.179
2020-03-09T05:46:55	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.179
2020-03-22T07:17:07	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.179
2020-04-20T10:39:03	TJAOI	Manual testing	50000	5000000						246	14.64

date	userid	compid	res64	spent (GHz-days)
1998-12-27T00:00:00	ANONYMOUS	v4_computers	D118CBB16FDC17A0	0.081

date

userid

compid

res64

spent (GHz-days)

1998-12-27T00:00:00

ANONYMOUS

v4_computers

D118CBB16FDC17A0

0.081

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)

10²

10³

10⁴

10⁵

10⁶

10²

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