M2235067 Mersenne number exponent details

Residue

Status

L-L

3CD79DF407593D06

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	13.2944	67.1642%	500000	15000000	0.1230	5.1919%	13.4174	68.8690%	1.7048%
PrimeNet	2⁵⁸	0.0172	62.0690%	10000	180000	0.0018	2.8714%	0.0190	63.1581%	1.0892%
GPU72	2⁶²	0.2749	64.5161%	11000	190000	0.0020	1.6578%	0.2769	65.1044%	0.5882%
Difference	+5	+13.0195	+2.6481%	+489000	+14810000	+0.1210	+3.5341%	+13.1406	+3.7646%	+3.7646%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.2944

67.1642%

500000

15000000

0.1230

5.1919%

13.4174

68.8690%

1.7048%

PrimeNet

2⁵⁸

0.0172

62.0690%

10000

180000

0.0018

2.8714%

0.0190

63.1581%

1.0892%

GPU72

2⁶²

0.2749

64.5161%

11000

190000

0.0020

1.6578%

0.2769

65.1044%

0.5882%

Difference

+13.0195

+2.6481%

+489000

+14810000

+0.1210

+3.5341%

+13.1406

+3.7646%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2235067	51473535390177885642475537	26	85.412	11514987110045892504 2³ × 3 × 1349533 × 355523821637	2013-06-24	1349533	355523821637	6,392,424	1,846.8	3,449.1

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2235067

51473535390177885642475537

85.412

11514987110045892504
2³ × 3 × 1349533 × 355523821637

2013-06-24

1349533

355523821637

6,392,424

1,846.8

3,449.1

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	-	-	0.282%
2010-10-30T19:40:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.782%
2011-01-13T18:33:00	Oscar Östlin		85000	1615000		-		-	-	0.016	-	-	2.467%
2016-04-17T12:47:20	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.192%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-02-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.017	-	-
2022-03-09T16:36:48	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.069	-	-
2009-01-11T09:30:00	Sturle Sunde	goldiek.ifi	2⁶⁰	2⁶¹		-	-	0.069	-	-
2012-04-20T20:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.137	-	-

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
		51473535390177885642475537	1	0.00000e+0
50000	5000000		9	0.772

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-24T17:54:00	Nathan Slaven	q6600	50000	5000000						3	0.257
2009-12-23T18:49:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.257
2011-10-05T12:05:00	S36049	Wolle5	50000	5000000						3	0.257
2013-06-24T06:50:00	Xyzzy	J			51473535390177885642475537	85.412		1		1	-

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	3CD79DF407593D06	0.147

date

userid

compid

res64

spent (GHz-days)

1999-03-15T00:00:00

ANONYMOUS

v4_computers

3CD79DF407593D06

0.147

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-10T12:03:22

Oliver Kruse

GTX-2

51473535390177885642475537

9C7011A677E579__

2017-11-20T15:59:10

kkmrkkblmbrbk

c4.xlarge

51473535390177885642475537

9C7011A677E579__

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 = 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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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