M2166289 Mersenne number exponent details

Residue

Status

L-L

287435A26F75CE0C

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	13.7165	67.1642%	500000	15000000	0.1230	5.1725%	13.8395	68.8626%	1.6984%
PrimeNet	2⁵⁸	0.0177	62.0690%	10000	180000	0.0018	2.8549%	0.0196	63.1519%	1.0829%
GPU72	2⁶²	0.2836	64.5161%	10000	160000	0.0017	1.5201%	0.2853	65.0555%	0.5394%
Difference	+5	+13.4329	+2.6481%	+490000	+14840000	+0.1213	+3.6523%	+13.5542	+3.8071%	+3.8071%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.7165

67.1642%

500000

15000000

0.1230

5.1725%

13.8395

68.8626%

1.6984%

PrimeNet

2⁵⁸

0.0177

62.0690%

10000

180000

0.0018

2.8549%

0.0196

63.1519%

1.0829%

GPU72

2⁶²

0.2836

64.5161%

10000

160000

0.0017

1.5201%

0.2853

65.0555%

0.5394%

Difference

+13.4329

+2.6481%

+490000

+14840000

+0.1213

+3.6523%

+13.5542

+3.8071%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2166289	35325696895362179599	20	64.937	8153505117591 3 × 2717835039197	2013-05-07	3	2717835039197	2.5581	14,117	26,367

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2166289

35325696895362179599

64.937

8153505117591
3 × 2717835039197

2013-05-07

2717835039197

2.5581

14,117

26,367

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.279%
2010-11-03T21:28:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.304%
2010-12-30T22:21:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.418%
2011-01-15T02:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.600%
2011-01-21T18:48:00	markr	tiny	120000	2370000		-		-	-	0.023	-	-	2.869%
2016-03-30T11:20:49	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.172%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2022-03-09T16:35:56	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.071	-	-
2009-01-04T03:10:00	Sturle Sunde	homilius.ifi	2⁶⁰	2⁶¹		-	-	0.071	-	-
2009-01-08T06:43:00	Sturle Sunde	homilius.ifi	2⁶¹	2⁶²		-	-	0.142	-	-
2013-01-23T08:20:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.453	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.121 GHz-days
Estimated T-Level:	1.150

Digits	B1	Curves	Complete	FacMiss
20	11000	23 / 100	0.230	79.361%
25	50000	23 / 280	0.082	92.100%

New Calculation Method

Total ECM effort:	2.121 GHz-days
Estimated T-Level:	1.150

Digits	B1	Complete	FacMiss
20	11000	0.918	39.939%
25	50000	0.086	91.799%
30	250000	0.005	99.459%

ECM Summary

B1	B2	factor	curves	GHz-days
		35325696895362179599	1	0.00000e+0
50000	5000000		9	0.769
50000	6423818		7	0.668
50000	6750000		7	0.684

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-07T18:47:00	axn	LittleMac	50000	5000000						3	0.256
2009-12-01T14:52:00	James Hintz	ryan	50000	5000000						3	0.256
2011-08-25T09:36:00	Lukasz Wrobel	WORK_lupo	50000	5000000						3	0.256
2013-05-07T16:18:00	hiems	Laptop			35325696895362179599	64.937		1		1	-
2022-06-04T11:06:06	Dylan Delgado	desktoplinux	50000	6750000						7	0.684
2022-08-03T05:17:46	debrouxl	dl380g9-1	50000	6423818						7	0.668

date	userid	compid	res64	spent (GHz-days)
1999-02-14T00:00:00	ANONYMOUS	v4_computers	287435A26F75CE0C	0.142

date

userid

compid

res64

spent (GHz-days)

1999-02-14T00:00:00

ANONYMOUS

v4_computers

287435A26F75CE0C

0.142

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-09T02:27:03

Oliver Kruse

GTX-3

35325696895362179599

87E75539738A56__

2017-11-23T07:22:24

kkmrkkblmbrbk

c4.xlarge

35325696895362179599

87E75539738A56__

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)

B1 = 120000, B2 = 2370000 (P-1 stage 2)

B1 = 120000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

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