M17038321 Mersenne number exponent details

Residue

Status

L-L

80B35088A0A40AF9

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	2⁶⁹	7.0070	63.7681%	220000	5500000	0.4192	4.0597%	7.4261	65.2390%	1.4709%
PrimeNet	2⁶⁵	0.4282	61.5385%	80000	2400000	0.1704	4.5316%	0.5986	63.2814%	1.7429%
GPU72	2⁶⁹	7.0070	63.7681%	120000	3200000	0.2376	3.2964%	7.2446	64.9624%	1.1943%
Difference	-	-	-	+100000	+2300000	+0.1815	+0.7634%	+0.1815	+0.2766%	+0.2766%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

7.0070

63.7681%

220000

5500000

0.4192

4.0597%

7.4261

65.2390%

1.4709%

PrimeNet

2⁶⁵

0.4282

61.5385%

80000

2400000

0.1704

4.5316%

0.5986

63.2814%

1.7429%

GPU72

2⁶⁹

7.0070

63.7681%

120000

3200000

0.2376

3.2964%

7.2446

64.9624%

1.1943%

Difference

+100000

+2300000

+0.1815

+0.7634%

+0.1815

+0.2766%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
17038321	1472719556273384688961	22	70.319	43217860382880 2⁵ × 3 × 5 × 31 × 41 × 70839661	2017-10-29	41	70839661	19.492	3.1868	5.9521

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

17038321

1472719556273384688961

70.319

43217860382880
2⁵ × 3 × 5 × 31 × 41 × 70839661

2017-10-29

70839661

19.492

3.1868

5.9521

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-11-16T00:00:00	ANONYMOUS	v4_computers	220000	5500000		-		-	-	0.419	-	-	4.060%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-02-04T00:00:00	Net_Force	v4_computers	2¹	2⁵⁸		-	-	0.002	-	-
2001-03-05T00:00:00	Net_Force	v4_computers	2¹	2⁵⁹		-	-	0.005	-	-
2001-08-04T00:00:00	Hatch	v4_computers	2¹	2⁶⁵		-	-	0.428	-	-
2016-03-17T13:00:23	Mark Rose	Manual testing	2⁶⁵	2⁶⁶		-	-	0.439	-	-
2014-09-15T13:05:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.877	-	-
2015-12-14T18:35:07	mikr	Manual testing	2⁶⁷	2⁶⁸		-	-	1.754	-	-
2017-10-22T21:37:21	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	3.509	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.866 GHz-days
Estimated T-Level:	0.050

Digits	B1	Curves	Complete	FacMiss
20	11000	1 / 100	0.010	99.000%
25	50000	1 / 280	0.004	99.643%

New Calculation Method

Total ECM effort:	0.866 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.038	96.227%
25	50000	0.004	99.645%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	1472719556273384688961	1	0.866

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-10-30T00:54:15	ATH	ec2-1xc	50000	5000000	1472719556273384688961	70.319	1	2		1	0.866

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2003-08-25T00:00:00	ANONYMOUS	v4_computers	80B35088A0A40AF9	9.70
2006-08-25T00:00:00	TheJudger	v4_computers	80B35088A0A40AF9	9.70

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 = 220000, B2 = 5500000 (P-1 stage 2)

B1 = 220000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁵⁹

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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