M2188181 Mersenne number exponent details

Residue

Status

L-L

6E23999486D3491D

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	13.5793	67.1642%	500000	15000000	0.1230	5.1787%	13.7023	68.8647%	1.7005%
PrimeNet	2⁵⁸	0.0175	62.0690%	10000	180000	0.0018	2.8602%	0.0194	63.1539%	1.0849%
GPU72	2⁶²	0.2808	64.5161%	11000	160000	0.0018	1.5699%	0.2826	65.0732%	0.5571%
Difference	+5	+13.2985	+2.6481%	+489000	+14840000	+0.1212	+3.6088%	+13.4197	+3.7915%	+3.7915%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.5793

67.1642%

500000

15000000

0.1230

5.1787%

13.7023

68.8647%

1.7005%

PrimeNet

2⁵⁸

0.0175

62.0690%

10000

180000

0.0018

2.8602%

0.0194

63.1539%

1.0849%

GPU72

2⁶²

0.2808

64.5161%

11000

160000

0.0018

1.5699%

0.2826

65.0732%

0.5571%

Difference

+13.2985

+2.6481%

+489000

+14840000

+0.1212

+3.6088%

+13.4197

+3.7915%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2188181	3096031529648805596377	22	71.391	707444112175548 2² × 3 × 11 × 1021 × 5249192059	2013-05-17	1021	5249192059	399.58	27.266	50.925

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2188181

3096031529648805596377

71.391

707444112175548
2² × 3 × 11 × 1021 × 5249192059

2013-05-17

1021

5249192059

399.58

27.266

50.925

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.280%
2010-11-04T10:39:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.238%
2010-11-08T22:12:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.418%
2011-01-12T17:41:00	markr	tiny	90000	1620000		-		-	-	0.017	-	-	2.489%
2016-03-29T11:23:24	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.179%

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	-	-
2022-03-09T16:35:58	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.070	-	-
2009-01-02T22:02:00	Sturle Sunde	ginjtje.ifi	2⁶⁰	2⁶¹		-	-	0.070	-	-
2009-01-08T07:55:00	Sturle Sunde	fungo.ifi	2⁶¹	2⁶²		-	-	0.140	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.467 GHz-days
Estimated T-Level:	0.800

Digits	B1	Curves	Complete	FacMiss
20	11000	16 / 100	0.160	85.146%
25	50000	16 / 280	0.057	94.436%

New Calculation Method

Total ECM effort:	1.467 GHz-days
Estimated T-Level:	0.800

Digits	B1	Complete	FacMiss
20	11000	0.638	52.844%
25	50000	0.059	94.256%
30	250000	0.004	99.626%

ECM Summary

B1	B2	factor	curves	GHz-days
		3096031529648805596377	1	0.00000e+0
50000	5000000		9	0.770
50000	6991079		7	0.697

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-10T22:16:00	ANONYMOUS	ghiottone	50000	5000000						3	0.257
2009-12-24T05:25:00	Wojciech Florek	perta	50000	5000000						3	0.257
2011-09-26T14:49:00	Lukasz Wrobel	i-2	50000	5000000						3	0.257
2013-05-17T18:30:00	jim f in mn	asus			3096031529648805596377	71.391		1		1	-
2022-06-29T07:31:18	debrouxl	o9020	50000	6991079						7	0.697

date	userid	compid	res64	spent (GHz-days)
1999-06-15T00:00:00	ANONYMOUS	v4_computers	6E23999486D3491D	0.144

date

userid

compid

res64

spent (GHz-days)

1999-06-15T00:00:00

ANONYMOUS

v4_computers

6E23999486D3491D

0.144

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-09T06:35:41

Oliver Kruse

GTX-0

3096031529648805596377

45E42467E0684C__

2017-11-19T11:28:42

kkmrkkblmbrbk

c4.xlarge

3096031529648805596377

45E42467E0684C__

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 = 90000, B2 = 1620000 (P-1 stage 2)

B1 = 90000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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