M2819329 Mersenne number exponent details

Residue

Status

L-L

511228B782C0DD27

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	10.5394	67.1642%	100000	3000000	0.0289	3.0410%	10.5683	68.1627%	0.9985%
PrimeNet	2⁵⁹	0.0272	62.7119%	12000	240000	0.0027	2.9307%	0.0300	63.8047%	1.0928%
GPU72	2⁶³	0.5661	65.0794%	15000	260000	0.0032	1.7921%	0.5693	65.7052%	0.6258%
Difference	+4	+9.9733	+2.0848%	+85000	+2740000	+0.0257	+1.2489%	+9.9990	+2.4575%	+2.4575%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

10.5394

67.1642%

100000

3000000

0.0289

3.0410%

10.5683

68.1627%

0.9985%

PrimeNet

2⁵⁹

0.0272

62.7119%

12000

240000

0.0027

2.9307%

0.0300

63.8047%

1.0928%

GPU72

2⁶³

0.5661

65.0794%

15000

260000

0.0032

1.7921%

0.5693

65.7052%

0.6258%

Difference

+9.9733

+2.0848%

+85000

+2740000

+0.0257

+1.2489%

+9.9990

+2.4575%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2819329	307506325082043079879	21	68.059	54535374389091 3 × 37 × 491309679181	2013-03-30	37	491309679181	36.246	2,997.8	5,599.1

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2819329

307506325082043079879

68.059

54535374389091
3 × 37 × 491309679181

2013-03-30

491309679181

36.246

2,997.8

5,599.1

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-28T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.301%
unknown			100000	3000000		-		-	-	0.029	-	-	3.041%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-02-13T18:10:00	Sturle Sunde	fizir.ifi	2⁶⁰	2⁶¹		-	-	0.054	-	-
2012-02-23T23:29:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.109	-	-
2013-01-10T10:21:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.348	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.626 GHz-days
Estimated T-Level:	0.300

Digits	B1	Curves	Complete	FacMiss
20	11000	6 / 100	0.060	94.148%
25	50000	6 / 280	0.021	97.876%

New Calculation Method

Total ECM effort:	0.626 GHz-days
Estimated T-Level:	0.300

Digits	B1	Complete	FacMiss
20	11000	0.231	79.392%
25	50000	0.021	97.887%
30	250000	0.001	99.865%

ECM Summary

B1	B2	factor	curves	GHz-days
		307506325082043079879	1	0.00000e+0
50000	5000000		6	0.626

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-21T07:04:00	Newro	home	50000	5000000						3	0.313
2010-10-25T13:46:00	wallu		50000	5000000						3	0.313
2013-03-30T10:01:00	KAMCOBILL	PC20			307506325082043079879	68.059		1		1	-

date	userid	compid	res64	spent (GHz-days)
1999-07-27T00:00:00	ANONYMOUS	v4_computers	511228B782C0DD27	0.218

date

userid

compid

res64

spent (GHz-days)

1999-07-27T00:00:00

ANONYMOUS

v4_computers

511228B782C0DD27

0.218

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-22T01:42:40

Oliver Kruse

GTX-2

307506325082043079879

51CB921461A5D2__

2017-12-06T23:45:07

kkmrkkblmbrbk

c4.xlarge

307506325082043079879

51CB921461A5D2__

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 = 100000, B2 = 3000000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁰

10¹

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