M1150879 Mersenne number exponent details

Residue

Status

L-L

E4B6569C0E8D9747

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	25.8185	68.6567%	6000000	240000000	0.8058	9.4598%	26.6242	71.6217%	2.9650%
PrimeNet	2⁵⁶	0.0083	62.5000%	5000	70000	0.0004	2.1633%	0.0087	63.3112%	0.8112%
GPU72	2⁶⁰	0.1335	65.0000%	5000	26000	0.0003	0.7709%	0.1337	65.2698%	0.2698%
Difference	+7	+25.6850	+3.6567%	+5995000	+239974000	+0.8055	+8.6888%	+26.4905	+6.3519%	+6.3519%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

25.8185

68.6567%

6000000

240000000

0.8058

9.4598%

26.6242

71.6217%

2.9650%

PrimeNet

2⁵⁶

0.0083

62.5000%

5000

70000

0.0004

2.1633%

0.0087

63.3112%

0.8112%

GPU72

2⁶⁰

0.1335

65.0000%

5000

26000

0.0003

0.7709%

0.1337

65.2698%

0.2698%

Difference

+25.6850

+3.6567%

+5995000

+239974000

+0.8055

+8.6888%

+26.4905

+6.3519%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1150879	82027186374570212626846441	26	86.084	35636755199534535180 2² × 3 × 5 × 17 × 31² × 36355874395069	2018-09-07	961	36355874395069	22,635,982	85,126	158,992
1150879	86626201847507033534809799	26	86.163	37634799943133480381 7 × 337 × 4397 × 337039 × 10765273	2015-10-18	337039	10765273	21,518,920	0.0389	0.0471

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1150879

82027186374570212626846441

86.084

35636755199534535180
2² × 3 × 5 × 17 × 31² × 36355874395069

2018-09-07

961

36355874395069

22,635,982

85,126

158,992

1150879

86626201847507033534809799

86.163

37634799943133480381
7 × 337 × 4397 × 337039 × 10765273

2015-10-18

337039

10765273

21,518,920

0.0389

0.0471

exponent	prime factors	composite factor	digits	bits*
1150879	82027186374570212626846441 86626201847507033534809799	71057036038665979211449084052778384848705601150753 59	52	172.247

exponent

prime factors

composite factor

digits

bits*

1150879

82027186374570212626846441
86626201847507033534809799

71057036038665979211449084052778384848705601150753
59

172.247

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2000-11-05T00:00:00	ANONYMOUS	v4_computers	50000	1000000		-		-	-	0.004	-	-	1.743%
2012-02-02T01:47:00	markr	tiny	500000	10000000		-		-	-	0.044	-	-	4.427%
2015-10-18T07:52:36	mikr	MSI	6000000	240000000	12		86626201847507033534809799	26	86.163	0.806	0.068	1.612	9.460%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2000-11-05T00:00:00

ANONYMOUS

v4_computers

50000

1000000

0.004

-

-

1.743%

2012-02-02T01:47:00

markr

tiny

500000

10000000

0.044

-

-

4.427%

2015-10-18T07:52:36

mikr

MSI

6000000

240000000

86626201847507033534809799

86.163

0.806

0.068

1.612

9.460%

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	-	-
2001-11-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.017	-	-
2003-05-04T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.033	-	-
2022-03-07T17:31:12	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.100	-	-
2009-04-15T05:20:00	Sturle Sunde	graun.ifi	2⁶⁰	2⁶¹		-	-	0.133	-	-
2011-05-09T14:44:00	Xyzzy	Manual testing	2⁶¹	2⁶²		-	-	0.267	-	-
2012-10-07T08:33:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.853	-	-
2014-12-28T15:46:00	Matthias Wurtinger	Manual testing	2⁶³	2⁶⁴		-	-	1.706	-	-
2015-01-10T22:22:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	3.247	-	-
2015-08-04T15:05:00	omylist	Manual testing	2⁶⁵	2⁶⁶		-	-	6.493	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.747 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:	17.747 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		214	7.580
50000	5000000	82027186374570212626846441	67	2.373
250000	25000000		44	7.793

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-10-09T15:50:00	Chad Davis	Bayes	50000	5000000						1	0.035
2008-06-14T17:35:00	James Heinrich	Q6600	50000	5000000						3	0.106
2009-01-03T02:42:00	Sturle Sunde	v24	50000	5000000						3	0.106
2009-06-05T10:45:00	S00030	pc-1002	50000	5000000						3	0.106
2009-09-12T16:38:00	Geoff Wing	GW1	50000	5000000						3	0.106
2010-01-05T08:34:00	Geoff Wing	GW1	50000	5000000						3	0.106
2010-06-29T23:20:00	unconnected	xp-lm	50000	5000000						3	0.106
2011-02-23T23:56:00	unconnected	can-01	50000	5000000						3	0.106
2011-11-09T21:29:00	OS1	Tina	50000	5000000						3	0.106
2012-07-17T11:56:00	soldake		50000	5000000						3	0.106
2013-01-29T11:41:00	OS1	Tina	50000	5000000						3	0.106
2013-10-01T05:05:00	OS1	Tina	50000	5000000						3	0.106
2014-02-05T22:05:00	OS1	Tina	50000	5000000						3	0.106
2014-03-08T20:32:00	Bruce	snowflake	50000	5000000						3	0.106
2014-07-25T20:20:00	Xyzzy	jv	50000	5000000						3	0.106
2015-03-09T23:56:00	arnaud	sgp-11-100	50000	5000000						3	0.106
2015-05-20T02:36:00	arnaud	sgp-11-100	50000	5000000						3	0.106
2015-08-31T15:37:00	WileECoyote	S120	50000	5000000						3	0.106
2017-09-01T10:40:47	TJAOI	Manual testing	50000	5000000						88	3.117
2018-09-07T12:10:47	TJAOI	Manual testing	50000	5000000	82027186374570212626846441	86.084	67	2		67	2.373
2018-09-07T12:10:47	TJAOI	Manual testing	50000	5000000						74	2.621
2020-08-21T10:52:00	TJAOI	Manual testing	250000	25000000						44	7.793

date	userid	compid	res64	spent (GHz-days)
2001-01-14T00:00:00	ANONYMOUS	v4_computers	E4B6569C0E8D9747	0.034

date

userid

compid

res64

spent (GHz-days)

2001-01-14T00:00:00

ANONYMOUS

v4_computers

E4B6569C0E8D9747

0.034

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-29T07:14:43

Oliver Kruse

GTX-1

86626201847507033534809799

4223C662E689BD__

2017-10-17T06:01:38

Oliver Kruse

Threadripper

86626201847507033534809799

4223C662E689BD__

2018-01-02T15:36:40

ATH

ec2-1xf

86626201847507033534809799

4223C662E689BD__

2018-09-08T12:47:33

ANONYMOUS

dory

82027186374570212626846441

86626201847507033534809799

88C18881D61028__

2018-09-11T13:34:34

Oliver Kruse

GTX-1

82027186374570212626846441

86626201847507033534809799

88C18881D61028__

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 = 6000000, B2 = 240000000 (P-1 stage 2)

B1 = 6000000 (P-1 stage 1)

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)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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