M2011913 Mersenne number exponent details

Residue

Status

L-L

8E7F3E8E92E954FF

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	14.7690	68.6567%	580000	15080000	0.1306	5.2203%	14.8996	70.2929%	1.6362%
PrimeNet	2⁵⁸	0.0191	63.7931%	9000	150000	0.0016	2.6100%	0.0207	64.7381%	0.9450%
GPU72	2⁶²	0.3054	66.1290%	8000	120000	0.0013	1.2722%	0.3067	66.5599%	0.4309%
Difference	+5	+14.4636	+2.5277%	+572000	+14960000	+0.1293	+3.9480%	+14.5929	+3.7330%	+3.7330%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.7690

68.6567%

580000

15080000

0.1306

5.2203%

14.8996

70.2929%

1.6362%

PrimeNet

2⁵⁸

0.0191

63.7931%

9000

150000

0.0016

2.6100%

0.0207

64.7381%

0.9450%

GPU72

2⁶²

0.3054

66.1290%

8000

120000

0.0013

1.2722%

0.3067

66.5599%

0.4309%

Difference

+14.4636

+2.5277%

+572000

+14960000

+0.1293

+3.9480%

+14.5929

+3.7330%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2011913	39722510605304437649	20	65.107	9871826119048 2³ × 67 × 18417586043	2015-06-29	67	18417586043	4.4688	95.666	178.68

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2011913

39722510605304437649

65.107

9871826119048
2³ × 67 × 18417586043

2015-06-29

18417586043

4.4688

95.666

178.68

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-04-28T00:00:00	Jocelyn Larouche	v4_computers	2000	2000		-		-	-	0.000	-	-	0.022%
2002-05-05T00:00:00	Jocelyn Larouche	v4_computers	3000	3000		-		-	-	0.000	-	-	0.040%
2003-01-25T00:00:00	ANONYMOUS	v4_computers	30000	547500		-		-	-	0.006	-	-	1.425%
2003-11-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.273%
2010-12-02T22:33:00	Jocelyn Larouche	Manual testing	201191	201191		-		-	-	0.019	-	-	1.329%
2013-10-09T03:32:00	David Campeau	i5-2500k	580000	15080000		-		-	-	0.131	-	-	5.220%
2016-03-17T19:19:32	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.127%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2022-03-09T07:16:45	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.076	-	-
2009-01-05T01:48:00	Sturle Sunde	corbusier.ifi	2⁶⁰	2⁶¹		-	-	0.076	-	-
2012-01-31T07:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.153	-	-
2013-02-11T20:23:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.488	-	-
2015-03-15T12:12:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.976	-	-
2015-03-15T12:12:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.857	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.224 GHz-days
Estimated T-Level:	1.850

Digits	B1	Curves	Complete	FacMiss
20	11000	37 / 100	0.370	68.945%
25	50000	37 / 280	0.132	87.601%

New Calculation Method

Total ECM effort:	3.224 GHz-days
Estimated T-Level:	1.850

Digits	B1	Complete	FacMiss
20	11000	1.218	29.590%
25	50000	0.110	89.618%
30	250000	0.007	99.326%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		29	2.455
50000	5000000	39722510605304437649	1	0.085
50000	6927937		7	0.685

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-29T06:46:00	Architects Cubed	m1_24	50000	5000000						3	0.254
2009-09-06T17:33:00	James Hintz	09_071509	50000	5000000						3	0.254
2011-02-09T17:30:00	Csaba Vágó	timigep	50000	5000000						3	0.254
2013-01-27T04:16:00	S00030	mac399	50000	5000000						3	0.254
2014-03-16T13:39:00	Bruce	snowflake	50000	5000000						3	0.254
2015-06-29T12:56:00	guru	w6	50000	5000000	39722510605304437649	65.107	1	2		1	0.085
2021-09-10T01:40:12	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.593
2021-12-25T20:07:43	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.593
2022-05-12T06:21:42	debrouxl	dl380g9-1	50000	6927937						7	0.685

date	userid	compid	res64	spent (GHz-days)
1999-06-06T00:00:00	ANONYMOUS	v4_computers	8E7F3E8E92E954FF	0.132

date

userid

compid

res64

spent (GHz-days)

1999-06-06T00:00:00

ANONYMOUS

v4_computers

8E7F3E8E92E954FF

0.132

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 = 580000, B2 = 15080000 (P-1 stage 2)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 580000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 201191 (P-1 stage 1)

B1 = 30000, B2 = 547500 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 3000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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