M2829913 Mersenne number exponent details

Residue

Status

L-L

263F4A88DA4A5CE3

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	10.4999	67.1642%	50000	1500000	0.0144	2.2394%	10.5144	67.8995%	0.7353%
PrimeNet	2⁵⁹	0.0271	62.7119%	12000	240000	0.0027	2.9327%	0.0299	63.8054%	1.0936%
GPU72	2⁶³	0.5640	65.0794%	16000	260000	0.0033	1.8265%	0.5673	65.7172%	0.6378%
Difference	+4	+9.9360	+2.0848%	+34000	+1240000	+0.0112	+0.4129%	+9.9471	+2.1823%	+2.1823%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

10.4999

67.1642%

50000

1500000

0.0144

2.2394%

10.5144

67.8995%

0.7353%

PrimeNet

2⁵⁹

0.0271

62.7119%

12000

240000

0.0027

2.9327%

0.0299

63.8054%

1.0936%

GPU72

2⁶³

0.5640

65.0794%

16000

260000

0.0033

1.8265%

0.5673

65.7172%

0.6378%

Difference

+9.9360

+2.0848%

+34000

+1240000

+0.0112

+0.4129%

+9.9471

+2.1823%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2829913	5478651435117536879201	22	72.214	967989375489200 2⁴ × 5² × 709 × 3413220647	2013-04-07	709	3413220647	387.69	20.826	38.898

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2829913

5478651435117536879201

72.214

967989375489200
2⁴ × 5² × 709 × 3413220647

2013-04-07

709

3413220647

387.69

20.826

38.898

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-03-27T00:00:00	ANONYMOUS	v4_computers	15000	161250		-		-	-	0.003	-	-	0.844%
2002-01-02T00:00:00	ANONYMOUS	v4_computers	20000	240000		-		-	-	0.004	-	-	1.056%
2002-01-02T00:00:00	ANONYMOUS	v4_computers	50000	1500000		-		-	-	0.014	-	-	2.239%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-04-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.027	-	-
2022-03-10T18:31:15	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.054	-	-
2009-02-12T21:09:00	Sturle Sunde	gonzo.ifi	2⁶⁰	2⁶¹		-	-	0.054	-	-
2012-02-12T07:15:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.109	-	-
2013-01-10T10:23:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.347	-	-

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
		5478651435117536879201	1	0.00000e+0
50000	5000000		6	0.626

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-21T05:14:00	James Hintz	12_060209	50000	5000000						3	0.313
2010-11-01T10:45:00	James Classen	towerofart	50000	5000000						3	0.313
2013-04-07T12:15:00	hiems	Laptop			5478651435117536879201	72.214		1		1	-

date	userid	compid	res64	spent (GHz-days)
1998-05-08T00:00:00	ANONYMOUS	v4_computers	263F4A88DA4A5CE3	0.219

date

userid

compid

res64

spent (GHz-days)

1998-05-08T00:00:00

ANONYMOUS

v4_computers

263F4A88DA4A5CE3

0.219

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-22T06:28:46

Oliver Kruse

GTX-3

5478651435117536879201

3350DCA343BDEF__

2017-12-07T04:32:01

kkmrkkblmbrbk

c4.xlarge

5478651435117536879201

3350DCA343BDEF__

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 = 50000, B2 = 1500000 (P-1 stage 2)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 240000 (P-1 stage 2)

B1 = 15000, B2 = 161250 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

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