M2418511 Mersenne number exponent details

Residue

Status

L-L

CFAD541B0A13C157

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	12.2860	67.1642%	2000000	60000000	0.5055	7.6213%	12.7915	69.6667%	2.5025%
PrimeNet	2⁵⁹	0.0318	62.7119%	10000	180000	0.0019	2.5221%	0.0336	63.6523%	0.9405%
GPU72	2⁶³	0.6599	65.0794%	10000	140000	0.0017	1.2769%	0.6616	65.5253%	0.4459%
Difference	+4	+11.6261	+2.0848%	+1990000	+59860000	+0.5038	+6.3444%	+12.1299	+4.1414%	+4.1414%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.2860

67.1642%

2000000

60000000

0.5055

7.6213%

12.7915

69.6667%

2.5025%

PrimeNet

2⁵⁹

0.0318

62.7119%

10000

180000

0.0019

2.5221%

0.0336

63.6523%

0.9405%

GPU72

2⁶³

0.6599

65.0794%

10000

140000

0.0017

1.2769%

0.6616

65.5253%

0.4459%

Difference

+11.6261

+2.0848%

+1990000

+59860000

+0.5038

+6.3444%

+12.1299

+4.1414%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2418511	29461360546778939606813238433	29	94.573	6090805571440224916656 2⁴ × 3² × 443 × 95479144272639593	2017-04-11	443	95479144272639593	2.706e+9	509,561,584	951,719,136

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2418511

29461360546778939606813238433

94.573

6090805571440224916656
2⁴ × 3² × 443 × 95479144272639593

2017-04-11

443

95479144272639593

2.706e+9

509,561,584

951,719,136

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.288%
2010-11-09T22:13:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.244%
2010-11-16T23:09:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.312%
2010-12-18T23:28:00	markr	tiny	95000	1923750		-		-	-	0.019	-	-	2.661%
2014-04-04T05:36:00	mikr	MSI	3102822	43439508		-		-	-	0.519	-	-	7.442%
2018-09-28T16:26:26	alpertron	Manual testing	2000000	60000000	12	-		-	-	0.505	-	-	7.621%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-02-12T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.016	-	-
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.032	-	-
2016-02-23T16:29:14	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.032	-	-
2009-01-11T15:57:00	Sturle Sunde	othello.ifi	2⁶⁰	2⁶¹		-	-	0.064	-	-
2012-06-04T14:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.127	-	-
2013-12-04T21:14:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.406	-	-
2015-02-27T20:40:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.812	-	-
2015-02-27T20:40:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.545	-	-
2015-10-22T10:17:20	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.090	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.406 GHz-days
Estimated T-Level:	1.350

Digits	B1	Curves	Complete	FacMiss
20	11000	27 / 100	0.270	76.234%
25	50000	27 / 280	0.096	90.792%

New Calculation Method

Total ECM effort:	2.406 GHz-days
Estimated T-Level:	1.350

Digits	B1	Complete	FacMiss
20	11000	0.871	41.855%
25	50000	0.079	92.430%
30	250000	0.005	99.516%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		24	2.139
50000	5000000	29461360546778939606813238433	3	0.267

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-02T16:41:00	paulie	iMac3.4	50000	5000000						3	0.267
2010-02-25T07:50:00	James Classen	towerofart	50000	5000000						3	0.267
2012-03-09T19:54:00	S36049	Wolle5	50000	5000000						3	0.267
2013-12-08T05:40:00	Andy Incline	Office-PC	50000	5000000						3	0.267
2015-06-30T23:35:00	guru	w1	50000	5000000						3	0.267
2016-02-20T14:03:20	Sintax	cloud	50000	5000000						3	0.267
2016-06-05T05:15:05	Bruce	Desk6	50000	5000000						3	0.267
2016-10-01T12:44:51	Bruce	Desk6	50000	5000000						3	0.267
2017-04-11T22:29:11	Bruce	Desk6	50000	5000000	29461360546778939606813238433	94.573	3	2		3	0.267

date	userid	compid	res64	spent (GHz-days)
1998-02-12T00:00:00	ANONYMOUS	v4_computers	CFAD541B0A13C157	0.163
1999-03-26T00:00:00	ANONYMOUS	v4_computers	CFAD541B0A13C157	0.163

date

userid

compid

res64

spent (GHz-days)

1998-02-12T00:00:00

ANONYMOUS

v4_computers

CFAD541B0A13C157

0.163

1999-03-26T00:00:00

ANONYMOUS

v4_computers

CFAD541B0A13C157

0.163

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 = 3102822, B2 = 43439508 (P-1 stage 2)

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

B1 = 3102822 (P-1 stage 1)

B1 = 2000000 (P-1 stage 1)

B1 = 95000, B2 = 1923750 (P-1 stage 2)

B1 = 95000 (P-1 stage 1)

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)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

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