M2778823 Mersenne number exponent details

Residue

Status

L-L

8680F4386DAFE74E

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	10.6930	67.1642%	110000	2392500	0.0262	2.9368%	10.7192	68.1285%	0.9643%
PrimeNet	2⁵⁹	0.0276	62.7119%	12000	220000	0.0026	2.8579%	0.0302	63.7775%	1.0656%
GPU72	2⁶³	0.5743	65.0794%	15000	240000	0.0031	1.7473%	0.5774	65.6895%	0.6102%
Difference	+4	+10.1186	+2.0848%	+95000	+2152500	+0.0232	+1.1895%	+10.1418	+2.4390%	+2.4390%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

10.6930

67.1642%

110000

2392500

0.0262

2.9368%

10.7192

68.1285%

0.9643%

PrimeNet

2⁵⁹

0.0276

62.7119%

12000

220000

0.0026

2.8579%

0.0302

63.7775%

1.0656%

GPU72

2⁶³

0.5743

65.0794%

15000

240000

0.0031

1.7473%

0.5774

65.6895%

0.6102%

Difference

+10.1186

+2.0848%

+95000

+2152500

+0.0232

+1.1895%

+10.1418

+2.4390%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2778823	271721199001367697167	21	67.881	48891418957121 13 × 101 × 41897 × 888761	2010-11-27	41897	888761	19.589	0.0099	0.0101

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2778823

271721199001367697167

67.881

48891418957121
13 × 101 × 41897 × 888761

2010-11-27

41897

888761

19.589

0.0099

0.0101

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-17T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.300%
2010-11-10T22:07:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.002	-	-	0.252%
2010-11-27T11:53:00	markr	tiny	110000	2392500			271721199001367697167	21	67.881	0.026	0.429	0.052	2.937%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-01-28T03:03:00	Sturle Sunde	ghini.ifi	2⁶⁰	2⁶¹		-	-	0.055	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.624 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:	0.624 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
50000	5000000		6	0.624

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-16T07:34:00	Jürgen Decker	Q9550_home	50000	5000000						3	0.312
2010-09-27T22:12:00	Kamil_Górski	thefault	50000	5000000						3	0.312

date	userid	compid	res64	spent (GHz-days)
1999-08-07T00:00:00	ANONYMOUS	v4_computers	8680F4386DAFE74E	0.215

date

userid

compid

res64

spent (GHz-days)

1999-08-07T00:00:00

ANONYMOUS

v4_computers

8680F4386DAFE74E

0.215

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-21T04:38:37

Oliver Kruse

GTX-3

271721199001367697167

9239399D69C2C6__

2017-12-06T15:43:13

trebor

Laptop

271721199001367697167

9239399D69C2C6__

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 = 110000, B2 = 2392500 (P-1 stage 2)

B1 = 110000 (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

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