M2478023 Mersenne number exponent details

Residue

Status

L-L

853C54489EECD0E2

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	11.9910	67.1642%	2382500	85770100	0.6965	8.1949%	12.6875	69.8550%	2.6909%
PrimeNet	2⁵⁹	0.0310	62.7119%	10000	180000	0.0019	2.5337%	0.0329	63.6566%	0.9448%
GPU72	2⁶³	0.6441	65.0794%	11000	160000	0.0019	1.3796%	0.6460	65.5611%	0.4818%
Difference	+4	+11.3469	+2.0848%	+2371500	+85610100	+0.6946	+6.8153%	+12.0415	+4.2939%	+4.2939%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

11.9910

67.1642%

2382500

85770100

0.6965

8.1949%

12.6875

69.8550%

2.6909%

PrimeNet

2⁵⁹

0.0310

62.7119%

10000

180000

0.0019

2.5337%

0.0329

63.6566%

0.9448%

GPU72

2⁶³

0.6441

65.0794%

11000

160000

0.0019

1.3796%

0.6460

65.5611%

0.4818%

Difference

+11.3469

+2.0848%

+2371500

+85610100

+0.6946

+6.8153%

+12.0415

+4.2939%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2478023	163795272297855814927525049903	30	97.048	33049586766921819314737 11² × 397 × 1747 × 2221 × 9437 × 18789479	2014-10-24	9437	18789479	1.440e+10	0.1039	0.1923

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2478023

163795272297855814927525049903

97.048

33049586766921819314737
11² × 397 × 1747 × 2221 × 9437 × 18789479

2014-10-24

9437

18789479

1.440e+10

0.1039

0.1923

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.290%
2003-10-31T00:00:00	Team Prime Rib	v4_computers	15000	228750		-		-	-	0.003	-	-	0.918%
2010-11-20T12:24:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.313%
2011-01-20T23:10:00	Oscar Östlin		95000	1947500		-		-	-	0.020	-	-	2.679%
2014-09-02T00:10:00	Jocelyn Larouche	Manual testing	120901	120901		-		-	-	0.012	-	-	1.053%
2014-10-24T19:46:00	mikr	MSI	2382500	85770100	12		163795272297855814927525049903	30	97.048	0.697	0.344	1.393	8.195%
2019-07-04T12:37:38	alpertron	Manual testing	2000000	60000000	12	-	skipped known factor: 163795272297855814927525049903	-	-	0.519	-	-	7.640%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-08-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.031	-	-
2022-03-10T05:53:00	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.062	-	-
2009-01-14T21:36:00	Sturle Sunde	hindemith.ifi	2⁶⁰	2⁶¹		-	-	0.062	-	-
2012-06-08T23:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.124	-	-
2013-01-23T08:29:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.396	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.102 GHz-days
Estimated T-Level:	0.600

Digits	B1	Curves	Complete	FacMiss
20	11000	12 / 100	0.120	88.638%
25	50000	12 / 280	0.043	95.797%

New Calculation Method

Total ECM effort:	1.102 GHz-days
Estimated T-Level:	0.600

Digits	B1	Complete	FacMiss
20	11000	0.387	67.903%
25	50000	0.035	96.562%
30	250000	0.002	99.785%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.102

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-12T14:35:00	Martti Järvi	SKYNET	50000	5000000						3	0.275
2010-03-22T20:56:00	James Classen	towerofart	50000	5000000						3	0.275
2012-06-05T04:33:00	Jacques MOLNE	Crazy_64	50000	5000000						3	0.275
2014-02-04T16:57:00	Kripke	Kripke	50000	5000000						3	0.275

date	userid	compid	res64	spent (GHz-days)
1999-10-21T00:00:00	MadPoo	v4_computers	853C54489EECD0E2	0.172

date

userid

compid

res64

spent (GHz-days)

1999-10-21T00:00:00

MadPoo

v4_computers

853C54489EECD0E2

0.172

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-14T02:44:28

Oliver Kruse

GTX-1

C9C4D6C3F76995__

2017-11-29T21:54:51

kkmrkkblmbrbk

old

163795272297855814927525049903

C9C4D6C3F76995__

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 = 2382500, B2 = 85770100 (P-1 stage 2)

B1 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 2382500 (P-1 stage 1)

B1 = 2000000 (P-1 stage 1)

B1 = 95000, B2 = 1947500 (P-1 stage 2)

B1 = 120901 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

B1 = 15000, B2 = 228750 (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