M2010329 Mersenne number exponent details

Residue

Status

L-L

D8703ACA12722378

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	14.7806	68.6567%	580000	15080000	0.1306	5.2198%	14.9112	70.2928%	1.6360%
PrimeNet	2⁵⁸	0.0191	63.7931%	9000	150000	0.0016	2.6096%	0.0207	64.7380%	0.9449%
GPU72	2⁶²	0.3056	66.1290%	8000	120000	0.0013	1.2720%	0.3069	66.5599%	0.4308%
Difference	+5	+14.4750	+2.5277%	+572000	+14960000	+0.1293	+3.9478%	+14.6043	+3.7329%	+3.7329%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.7806

68.6567%

580000

15080000

0.1306

5.2198%

14.9112

70.2928%

1.6360%

PrimeNet

2⁵⁸

0.0191

63.7931%

9000

150000

0.0016

2.6096%

0.0207

64.7380%

0.9449%

GPU72

2⁶²

0.3056

66.1290%

8000

120000

0.0013

1.2720%

0.3069

66.5599%

0.4308%

Difference

+14.4750

+2.5277%

+572000

+14960000

+0.1293

+3.9478%

+14.6043

+3.7329%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2010329	174078445645502436061241	24	77.204	43296009172006780 2² × 5 × 7 × 2044351 × 151274027	2017-10-06	2044351	151274027	21,685	0.9700	1.4676

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2010329

174078445645502436061241

77.204

43296009172006780
2² × 5 × 7 × 2044351 × 151274027

2017-10-06

2044351

151274027

21,685

0.9700

1.4676

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%
2010-11-29T23:20:00	Jocelyn Larouche	Manual testing	201032	201032		-		-	-	0.019	-	-	1.328%
2013-10-08T12:24:00	David Campeau	i5-2500k	580000	15080000		-		-	-	0.131	-	-	5.220%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15T00:00:00	Stephen Wood	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2016-02-23T16:29:03	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.057	-	-
2009-01-04T07:10:00	Sturle Sunde	corbusier.ifi	2⁶⁰	2⁶¹		-	-	0.076	-	-
2011-12-28T01:20:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.153	-	-
2013-02-11T20:22:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.488	-	-
2015-03-15T12:12:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.977	-	-
2015-03-15T12:12:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.859	-	-
2015-10-28T09:42:35	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.717	-	-
2016-03-14T03:48:36	Smok_bmv	Manual testing	2⁶⁶	2⁶⁷		-	-	7.434	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.265 GHz-days
Estimated T-Level:	2.400

Digits	B1	Curves	Complete	FacMiss
20	11000	48 / 100	0.480	61.729%
25	50000	48 / 280	0.171	84.220%

New Calculation Method

Total ECM effort:	4.265 GHz-days
Estimated T-Level:	2.400

Digits	B1	Complete	FacMiss
20	11000	1.891	15.092%
25	50000	0.176	83.897%
30	250000	0.011	98.895%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	2.793
50000	5000000	174078445645502436061241	1	0.085
50000	7070138		7	0.692
50000	7150000		7	0.696

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-29T02:21:00	mognuts	hallowes	50000	5000000						3	0.254
2009-09-06T04:33:00	James Hintz	08_071509	50000	5000000						3	0.254
2011-02-05T05:03:00	Lupo	yorick	50000	5000000						3	0.254
2013-01-24T07:23:00	S00030	mac399	50000	5000000						3	0.254
2014-03-16T08:21:00	Bruce	snowflake	50000	5000000						3	0.254
2015-06-29T02:32:00	guru	w1	50000	5000000						3	0.254
2015-08-27T01:21:00	mikr	MSI	50000	5000000						12	1.016
2017-01-25T07:06:53	ANONYMOUS	Main-PC	50000	5000000						3	0.254
2017-10-06T18:24:48	Sid & Andy	Woody	50000	5000000	174078445645502436061241	77.204	1	2		1	0.085
2022-06-08T08:13:53	debrouxl	dl380g9-1	50000	7150000						7	0.696
2022-08-12T01:54:51	debrouxl	o9020	50000	7070138						7	0.692

date	userid	compid	res64	spent (GHz-days)
1999-03-26T00:00:00	Stephen Wood	v4_computers	D8703ACA12722378	0.132
2016-05-05T08:34:00	MadPoo	Manual testing	D8703ACA12722378	0.132

date

userid

compid

res64

spent (GHz-days)

1999-03-26T00:00:00

Stephen Wood

v4_computers

D8703ACA12722378

0.132

2016-05-05T08:34:00

MadPoo

Manual testing

D8703ACA12722378

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 = 580000 (P-1 stage 1)

B1 = 201032 (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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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