M2228341 Mersenne number exponent details

Residue

Status

L-L

7E03E80788ECF4A4

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	13.3345	67.1642%	1000000	106000000	0.6407	7.7349%	13.9753	69.7040%	2.5398%
PrimeNet	2⁵⁸	0.0172	62.0690%	10000	180000	0.0018	2.8698%	0.0191	63.1575%	1.0886%
GPU72	2⁶²	0.2757	64.5161%	11000	180000	0.0019	1.6311%	0.2776	65.0949%	0.5788%
Difference	+5	+13.0588	+2.6481%	+989000	+105820000	+0.6388	+6.1038%	+13.6977	+4.6091%	+4.6091%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.3345

67.1642%

1000000

106000000

0.6407

7.7349%

13.9753

69.7040%

2.5398%

PrimeNet

2⁵⁸

0.0172

62.0690%

10000

180000

0.0018

2.8698%

0.0191

63.1575%

1.0886%

GPU72

2⁶²

0.2757

64.5161%

11000

180000

0.0019

1.6311%

0.2776

65.0949%

0.5788%

Difference

+13.0588

+2.6481%

+989000

+105820000

+0.6388

+6.1038%

+13.6977

+4.6091%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2228341	2155414006017684936463	22	70.868	483636482481291 3 × 150559 × 1070757383	2013-06-25	150559	1070757383	139.08	5.5754	10.388
2228341	861155517044326278037663	24	79.511	193227947841987891 3² × 7 × 29 × 31 × 41 × 47 × 181 × 9781589	2016-04-09	181	9781589	77,670	0.0508	0.0949

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2228341

2155414006017684936463

70.868

483636482481291
3 × 150559 × 1070757383

2013-06-25

150559

1070757383

139.08

5.5754

10.388

2228341

861155517044326278037663

79.511

193227947841987891
3² × 7 × 29 × 31 × 41 × 47 × 181 × 9781589

2016-04-09

181

9781589

77,670

0.0508

0.0949

exponent	prime factors	composite factor	digits	bits*
2228341	2155414006017684936463 861155517044326278037663	1856146662796742063119919849489715342476005969	46	150.379

exponent

prime factors

composite factor

digits

bits*

2228341

2155414006017684936463
861155517044326278037663

1856146662796742063119919849489715342476005969

150.379

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.281%
2010-10-24T21:41:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.782%
2011-01-13T09:53:00	Oscar Östlin		85000	1615000		-		-	-	0.016	-	-	2.466%
2016-04-09T13:17:14	alpertron	Manual testing	500000	15000000	12		861155517044326278037663	24	79.511	0.123	0.293	0.246	5.190%
2021-06-29T22:18:03	Dylan Delgado	laptop-ryzen73700	1000000	106000000		-	skipped known factor: 861155517044326278037663	-	-	0.641	-	-	7.735%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-01-11T05:41:00	Sturle Sunde	gopher.ifi	2⁶⁰	2⁶¹		-	-	0.069	-	-
2012-04-20T06:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.138	-	-
2013-01-23T08:24:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.441	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.772 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	0.772 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.346	70.740%
25	50000	0.032	96.848%
30	250000	0.002	99.798%

ECM Summary

B1	B2	factor	curves	GHz-days
		2155414006017684936463	1	0.00000e+0
50000	5000000		9	0.772

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-13T10:23:00	SubPrime	c2d0	50000	5000000						3	0.257
2009-12-20T14:45:00	James Classen	towerofart	50000	5000000						3	0.257
2011-10-03T09:14:00	Dmitry B. Khachaturov	dix-home	50000	5000000						3	0.257
2013-06-25T10:25:00	hiems	Laptop			2155414006017684936463	70.868		1		1	-

date	userid	compid	res64	spent (GHz-days)
1999-05-02T00:00:00	ANONYMOUS	v4_computers	7E03E80788ECF4A4	0.147

date

userid

compid

res64

spent (GHz-days)

1999-05-02T00:00:00

ANONYMOUS

v4_computers

7E03E80788ECF4A4

0.147

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-09T23:01:30

Oliver Kruse

GTX-2

2155414006017684936463

861155517044326278037663

9742A362DFD25225

2017-10-18T01:21:16

Oliver Kruse

GTX-3

2155414006017684936463

861155517044326278037663

A904AA9E8B9087__

2017-11-20T15:23:38

kkmrkkblmbrbk

old

2155414006017684936463

861155517044326278037663

A904AA9E8B9087__

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 = 1000000, B2 = 106000000 (P-1 stage 2)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 85000, B2 = 1615000 (P-1 stage 2)

B1 = 85000 (P-1 stage 1)

B1 = 75011 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

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