M1163473 Mersenne number exponent details

Residue

Status

L-L

921CEE5C11A73FB8

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	25.5390	68.6567%	500000	10000000	0.0452	4.4332%	25.5842	70.0462%	1.3895%
PrimeNet	2⁵⁶	0.0083	62.5000%	5000	80000	0.0004	2.2556%	0.0087	63.3458%	0.8458%
GPU72	2⁶⁰	0.1320	65.0000%	5000	28000	0.0003	0.7971%	0.1323	65.2790%	0.2790%
Difference	+7	+25.4070	+3.6567%	+495000	+9972000	+0.0450	+3.6361%	+25.4519	+4.7672%	+4.7672%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

25.5390

68.6567%

500000

10000000

0.0452

4.4332%

25.5842

70.0462%

1.3895%

PrimeNet

2⁵⁶

0.0083

62.5000%

5000

80000

0.0004

2.2556%

0.0087

63.3458%

0.8458%

GPU72

2⁶⁰

0.1320

65.0000%

5000

28000

0.0003

0.7971%

0.1323

65.2790%

0.2790%

Difference

+25.4070

+3.6567%

+495000

+9972000

+0.0450

+3.6361%

+25.4519

+4.7672%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1163473	14103267838208525842972753	26	83.544	6060848785579263912 2³ × 3 × 19² × 191 × 3662533771313	2015-12-02	361	3662533771313	1,994,195	8,873.1	16,572

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1163473

14103267838208525842972753

83.544

6060848785579263912
2³ × 3 × 19² × 191 × 3662533771313

2015-12-02

361

3662533771313

1,994,195

8,873.1

16,572

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2002-03-16T00:00:00	Jocelyn Larouche	v4_computers	1000	1000		-		-	-	4.44667e-5	-	-	0.005%
2002-06-09T00:00:00	ANONYMOUS	v4_computers	50000	1000000		-		-	-	0.005	-	-	1.746%
2012-02-05T23:09:00	markr	tiny	500000	10000000		-		-	-	0.045	-	-	4.433%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2002-03-16T00:00:00

Jocelyn Larouche

v4_computers

1000

4.44667e-5

-

-

0.005%

2002-06-09T00:00:00

ANONYMOUS

v4_computers

50000

1000000

0.005

-

-

1.746%

2012-02-05T23:09:00

markr

tiny

500000

10000000

0.045

-

-

4.433%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-07-12T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.008	-	-
2001-11-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.017	-	-
2003-05-04T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.033	-	-
2022-03-07T17:31:14	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.099	-	-
2009-04-09T04:56:00	Sturle Sunde	bruckner.ifi	2⁶⁰	2⁶¹		-	-	0.132	-	-
2011-05-09T14:45:00	Xyzzy	Manual testing	2⁶¹	2⁶²		-	-	0.264	-	-
2012-10-11T11:55:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.844	-	-
2014-12-31T09:45:00	Matthias Wurtinger	Manual testing	2⁶³	2⁶⁴		-	-	1.687	-	-
2015-01-03T11:50:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	3.211	-	-
2015-09-17T03:04:00	omylist	Manual testing	2⁶⁵	2⁶⁶		-	-	6.423	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.391 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	325 / 100	3.250	3.815%
25	50000	325 / 280	1.161	31.261%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	18.391 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	12.731	0.000%
25	50000	1.349	25.941%
30	250000	0.108	89.793%
35	1000000	0.007	99.295%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		280	10.28
50000	5000000	14103267838208525842972753	1	0.037
250000	25000000		44	8.076

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-10-10T17:34:00	robcreid	robcreid_asus	50000	5000000						1	0.037
2008-06-23T05:28:00	Sturle Sunde	v1	50000	5000000						3	0.110
2009-01-08T18:27:00	Sturle Sunde	v23	50000	5000000						3	0.110
2009-06-15T08:50:00	Lackó	Iroda_Eva	50000	5000000						3	0.110
2009-09-17T18:59:00	SubPrime	c2d0	50000	5000000						3	0.110
2010-01-14T20:24:00	ClknGo Software Corp	cngs1	50000	5000000						3	0.110
2010-07-15T10:35:00	unconnected	xp-lm	50000	5000000						3	0.110
2011-03-06T03:18:00	unconnected	can-01	50000	5000000						3	0.110
2011-11-20T09:39:00	OS1	Tina	50000	5000000						3	0.110
2012-07-26T03:02:00	soldake		50000	5000000						3	0.110
2013-02-19T13:03:00	OS1	Tina	50000	5000000						3	0.110
2013-10-25T02:00:00	jim f in mn	asus	50000	5000000						3	0.110
2014-02-28T23:18:00	Bruce	snowflake	50000	5000000						3	0.110
2014-03-09T21:13:00	Bruce	snowflake	50000	5000000						3	0.110
2014-09-09T19:12:00	OS1	Tina	50000	5000000						3	0.110
2015-03-07T20:10:00	Bruce	desk16	50000	5000000						3	0.110
2015-05-25T15:56:00	Jason U	Dell-Win7	50000	5000000						3	0.110
2015-09-18T18:05:00	Jason U	Dell-Win7	50000	5000000						3	0.110
2015-12-02T16:40:57	Bruce	Desk9	50000	5000000	14103267838208525842972753	83.544	1	2		1	0.037
2017-08-25T10:19:16	TJAOI	Manual testing	50000	5000000						87	3.194
2018-09-07T12:13:26	TJAOI	Manual testing	50000	5000000						141	5.176
2020-10-23T07:50:42	TJAOI	Manual testing	250000	25000000						44	8.076

date	userid	compid	res64	spent (GHz-days)
2002-07-27T00:00:00	Ethan O'Connor	v4_computers	921CEE5C11A73FB8	0.036

date

userid

compid

res64

spent (GHz-days)

2002-07-27T00:00:00

Ethan O'Connor

v4_computers

921CEE5C11A73FB8

0.036

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 = 500000, B2 = 10000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 50000, B2 = 1000000 (P-1 stage 2)

B1 = 50000 (P-1 stage 1)

B1 = 1000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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