M16309589 Mersenne number exponent details

Residue

Status

L-L

4E6097079516CDC5

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	1.8219	64.1791%	180000	2160000	0.2282	3.9650%	2.0501	65.5994%	1.4203%
PrimeNet	2⁶⁵	0.4473	63.0769%	70000	2200000	0.1475	4.3302%	0.5948	64.6758%	1.5988%
GPU72	2⁶⁹	7.3200	65.2174%	110000	3000000	0.2121	3.1813%	7.5321	66.3239%	1.1066%
Difference	-2	-5.4982	-1.0383%	+70000	-840000	+0.0162	+0.7837%	-5.4820	-0.7245%	-0.7245%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

1.8219

64.1791%

180000

2160000

0.2282

3.9650%

2.0501

65.5994%

1.4203%

PrimeNet

2⁶⁵

0.4473

63.0769%

70000

2200000

0.1475

4.3302%

0.5948

64.6758%

1.5988%

GPU72

2⁶⁹

7.3200

65.2174%

110000

3000000

0.2121

3.1813%

7.5321

66.3239%

1.1066%

Difference

-2

-5.4982

-1.0383%

+70000

-840000

+0.0162

+0.7837%

-5.4820

-0.7245%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
16309589	1096223465124083478403337359	28	89.825	33606716426884928811 3 × 11 × 31 × 67 × 223 × 2198724329177	2017-02-26	223	2198724329177	12,463,917	94,980	177,396

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

16309589

1096223465124083478403337359

89.825

33606716426884928811
3 × 11 × 31 × 67 × 223 × 2198724329177

2017-02-26

223

2198724329177

12,463,917

94,980

177,396

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-08-24T00:00:00	ANONYMOUS	v4_computers	180000	2160000		-		-	-	0.228	-	-	3.965%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-08-24T00:00:00	Mike Curtis	v4_computers	2¹	2⁶¹		-	-	0.019	-	-
2002-01-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁵		-	-	0.447	-	-
2016-03-16T02:34:19	Mark Rose	Manual testing	2⁶⁵	2⁶⁶		-	-	0.458	-	-
2014-08-18T15:07:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.916	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.831 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:	0.831 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.032	96.826%
25	50000	0.003	99.709%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	1096223465124083478403337359	1	0.831

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-02-26T20:32:15	Bruce	mini	50000	5000000	1096223465124083478403337359	89.825	1	2		1	0.831

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-10-12T00:00:00	ANONYMOUS	v4_computers	4E6097079516CDC5	8.918
2006-04-28T00:00:00	ebravick	v4_computers	4E6097079516CDC5	8.918

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 = 180000, B2 = 2160000 (P-1 stage 2)

B1 = 180000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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