M2553233 Mersenne number exponent details

Residue

Status

L-L

BB3C0C850C961E28

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	11.6378	67.1642%	2000000	60000000	0.5190	7.6637%	12.1567	69.6806%	2.5164%
PrimeNet	2⁵⁹	0.0301	62.7119%	11000	200000	0.0021	2.6859%	0.0322	63.7134%	1.0015%
GPU72	2⁶³	0.6251	65.0794%	12000	180000	0.0021	1.4784%	0.6272	65.5956%	0.5163%
Difference	+4	+11.0127	+2.0848%	+1988000	+59820000	+0.5168	+6.1853%	+11.5295	+4.0850%	+4.0850%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

11.6378

67.1642%

2000000

60000000

0.5190

7.6637%

12.1567

69.6806%

2.5164%

PrimeNet

2⁵⁹

0.0301

62.7119%

11000

200000

0.0021

2.6859%

0.0322

63.7134%

1.0015%

GPU72

2⁶³

0.6251

65.0794%

12000

180000

0.0021

1.4784%

0.6272

65.5956%

0.5163%

Difference

+11.0127

+2.0848%

+1988000

+59820000

+0.5168

+6.1853%

+11.5295

+4.0850%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2553233	420842376313398261881	21	68.512	82413625453180 2² × 5 × 7 × 23 × 1201 × 21310819	2015-08-10	1201	21310819	41.792	0.1169	0.2181

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2553233

420842376313398261881

68.512

82413625453180
2² × 5 × 7 × 23 × 1201 × 21310819

2015-08-10

1201

21310819

41.792

0.1169

0.2181

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-23T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.293%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	198750		-		-	-	0.003	-	-	0.884%
2010-12-19T21:44:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.315%
2011-01-03T14:35:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.433%
2011-01-09T14:30:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.620%
2011-04-09T06:24:00	James Heinrich	WHS	175000	4068750		-		-	-	0.039	-	-	3.529%
2019-07-04T12:40:31	alpertron	Manual testing	2000000	60000000	12	-	skipped known factor: 420842376313398261881	-	-	0.519	-	-	7.664%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2022-03-11T02:04:59	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.060	-	-
2009-01-31T01:47:00	Sturle Sunde	goomba.ifi	2⁶⁰	2⁶¹		-	-	0.060	-	-
2012-06-16T16:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.120	-	-
2013-01-14T11:53:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.384	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.769	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.463	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.291 GHz-days
Estimated T-Level:	0.700

Digits	B1	Curves	Complete	FacMiss
20	11000	14 / 100	0.140	86.875%
25	50000	14 / 280	0.050	95.114%

New Calculation Method

Total ECM effort:	1.291 GHz-days
Estimated T-Level:	0.700

Digits	B1	Complete	FacMiss
20	11000	0.452	63.660%
25	50000	0.041	96.001%
30	250000	0.003	99.749%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.107
50000	5000000	420842376313398261881	2	0.184

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-15T09:43:00	Smurgs	Praca	50000	5000000						3	0.277
2010-05-07T17:50:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.277
2012-10-08T05:56:00	Bud	annan	50000	5000000						3	0.277
2014-04-10T06:49:00	Andy Incline	Office-PC	50000	5000000						3	0.277
2015-08-10T17:05:00	guru	w6	50000	5000000	420842376313398261881	68.512	2	2		2	0.184

date	userid	compid	res64	spent (GHz-days)
1999-05-02T00:00:00	ANONYMOUS	v4_computers	BB3C0C850C961E28	0.177

date

userid

compid

res64

spent (GHz-days)

1999-05-02T00:00:00

ANONYMOUS

v4_computers

BB3C0C850C961E28

0.177

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-14T22:20:56

Oliver Kruse

GTX-1

0D763F5B213054__

2017-12-01T10:55:58

ATH

ec2-1xf

420842376313398261881

0D763F5B213054__

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 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 175000, B2 = 4068750 (P-1 stage 2)

B1 = 175000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 198750 (P-1 stage 2)

B1 = 20000 (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

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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