M1837529 Mersenne number exponent details

Residue

Status

L-L

53BE32159809A9A6

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	2⁶⁸	32.4375	69.1176%	1837529	183752900	0.9242	8.0202%	33.3617	71.5945%	2.4768%
PrimeNet	2⁵⁷	0.0104	63.1579%	8000	150000	0.0012	2.8813%	0.0117	64.2194%	1.0615%
GPU72	2⁶¹	0.1672	65.5738%	9000	140000	0.0013	1.5959%	0.1684	66.1232%	0.5494%
Difference	+7	+32.2703	+3.5439%	+1828529	+183612900	+0.9229	+6.4242%	+33.1933	+5.4713%	+5.4713%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

32.4375

69.1176%

1837529

183752900

0.9242

8.0202%

33.3617

71.5945%

2.4768%

PrimeNet

2⁵⁷

0.0104

63.1579%

8000

150000

0.0012

2.8813%

0.0117

64.2194%

1.0615%

GPU72

2⁶¹

0.1672

65.5738%

9000

140000

0.0013

1.5959%

0.1684

66.1232%

0.5494%

Difference

+32.2703

+3.5439%

+1828529

+183612900

+0.9229

+6.4242%

+33.1933

+5.4713%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1837529	14888869025352094071919	23	73.657	4051328992726671 3² × 31 × 383 × 37913557303	2020-02-25	383	37913557303	1,796.1	162.49	303.48
1837529	537755869921228016803991	24	78.831	146325818509865155 5 × 7 × 53 × 103 × 557 × 1374942791	2021-04-30	557	1374942791	46,691	5.8927	11.006

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1837529

14888869025352094071919

73.657

4051328992726671
3² × 31 × 383 × 37913557303

2020-02-25

383

37913557303

1,796.1

162.49

303.48

1837529

537755869921228016803991

78.831

146325818509865155
5 × 7 × 53 × 103 × 557 × 1374942791

2021-04-30

557

1374942791

46,691

5.8927

11.006

exponent	prime factors	composite factor	digits	bits*
1837529	14888869025352094071919 537755869921228016803991	8006576714871441663294030362492157147680228729	46	152.488

exponent

prime factors

composite factor

digits

bits*

1837529

14888869025352094071919
537755869921228016803991

8006576714871441663294030362492157147680228729

152.488

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2011-02-08T15:59:00	Carsten Kossendey	leela	100000	1675000		-		-	-	0.015	-	-	2.211%
2014-05-19T21:00:00	Jocelyn Larouche	Manual testing	134930	134930		-		-	-	0.011	-	-	0.925%
2014-09-22T21:00:00	Jocelyn Larouche	Manual testing	169860	169860		-		-	-	0.013	-	-	1.050%
2015-07-02T21:01:00	mikr	MSI	2780000	91760000		-		-	-	0.600	-	-	7.493%
2018-08-13T11:55:02	Jocelyn Larouche	low 4M	1837529	183752900	12	-		-	-	0.924	-	-	8.020%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2011-02-08T15:59:00

Carsten Kossendey

leela

100000

1675000

0.015

-

-

2.211%

2014-05-19T21:00:00

Jocelyn Larouche

Manual testing

134930

0.011

-

-

0.925%

2014-09-22T21:00:00

Jocelyn Larouche

Manual testing

169860

0.013

-

-

1.050%

2015-07-02T21:01:00

mikr

MSI

2780000

91760000

0.600

-

-

7.493%

2018-08-13T11:55:02

Jocelyn Larouche

low 4M

1837529

183752900

0.924

-

-

8.020%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-
2016-02-23T16:28:54	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.063	-	-
2010-04-16T12:29:00	Architects Cubed	a3_lm	2⁶⁰	2⁶¹		-	-	0.084	-	-
2016-02-23T16:28:54	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.167	-	-
2011-01-21T16:11:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.869	-	-
2016-02-23T16:28:54	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.534	-	-
2015-04-26T21:13:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.068	-	-
2015-04-26T21:13:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.033	-	-
2015-09-05T13:49:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.067	-	-
2018-01-22T18:13:16	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.133	-	-
2019-06-17T12:14:59	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	16.27	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.639 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	18.639 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.424	0.022%
25	50000	0.763	46.646%
30	250000	0.047	95.398%
35	1000000	0.002	99.784%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		102	7.048
50000	5000000	14888869025352094071919	2	0.138
50000	6600000		95	7.401
50000	6600000	537755869921228016803991	52	4.051

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-10-08T02:19:00	Scott Kurowski	UW1	50000	5000000						3	0.207
2009-07-19T00:07:00	SubPrime	mysql0	50000	5000000						3	0.207
2010-11-16T07:33:00	Lupo	yorick	50000	5000000						3	0.207
2012-06-03T06:02:00	smoky	mac	50000	5000000						3	0.207
2013-08-30T07:25:00	OS1	L3	50000	5000000						3	0.207
2014-05-12T19:48:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-11-12T19:01:00	mikr	MSI	50000	5000000						12	0.829
2016-06-01T17:00:57	Bruce	DESK3	50000	5000000						3	0.207
2016-09-08T02:57:39	Bruce	DESK3	50000	5000000						3	0.207
2016-11-15T05:35:47	Bruce	DESK3	50000	5000000						3	0.207
2017-01-13T15:53:03	Bruce	DESK3	50000	5000000						3	0.207
2017-05-14T15:38:25	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2017-12-10T04:21:23	Bruce	DESK3	50000	5000000						3	0.207
2018-02-11T05:49:29	Bruce	DESK3	50000	5000000						3	0.207
2019-11-23T16:29:34	arnaud	CHAMOT06	50000	5000000						3	0.207
2019-11-26T01:31:28	cappy95833	HomePC	50000	5000000						3	0.207
2019-11-28T21:40:50	penlu	grizzly	50000	5000000						3	0.207
2019-12-02T08:55:27	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.207
2019-12-11T20:31:41	mnd9	colab	50000	5000000						3	0.207
2019-12-15T01:32:21	J.R. Allen	lapacer	50000	5000000						3	0.207
2019-12-27T17:39:41	mnd9	50871b	50000	5000000						3	0.207
2019-12-31T06:11:34	TheJudger	myECM	50000	5000000						3	0.207
2020-01-03T03:42:02	Keysarecool	Boat_Anchor	50000	5000000						3	0.207
2020-01-05T15:45:29	TheJudger	myECM	50000	5000000						3	0.207
2020-01-05T21:58:46	TheJudger	Sinope	50000	5000000						3	0.207
2020-01-13T12:03:51	daveward2005	Davy	50000	5000000						3	0.207
2020-01-20T12:15:21	daveward2005	Davy	50000	5000000						3	0.207
2020-01-26T05:11:36	EricP	Cannonfodder	50000	5000000						3	0.207
2020-02-05T21:37:29	Massimo Cappelli (ik5pwa)	maxlinux_3	50000	5000000						3	0.207
2020-02-12T17:36:09	cappy95833	HomePC	50000	5000000						3	0.207
2020-02-19T21:04:33	mnd9	colab	50000	5000000						3	0.207
2020-02-26T04:31:19	MarkS	desktop-i7	50000	5000000	14888869025352094071919	73.657	2	2	4022330489134550	2	0.138
2021-04-30T08:12:46	TJAOI	Manual testing	50000	6600000	537755869921228016803991	78.831	52	2		52	4.051
2021-04-30T08:12:46	TJAOI	Manual testing	50000	6600000						95	7.401

date	userid	compid	res64	spent (GHz-days)
1998-12-13T00:00:00	ANONYMOUS	v4_computers	53BE32159809A9A6	0.100
2015-07-10T01:00:00	MadPoo	Manual testing	53BE32159809A9A6	0.100

date

userid

compid

res64

spent (GHz-days)

1998-12-13T00:00:00

ANONYMOUS

v4_computers

53BE32159809A9A6

0.100

2015-07-10T01:00:00

MadPoo

Manual testing

53BE32159809A9A6

0.100

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 = 1837529, B2 = 183752900 (P-1 stage 2)

B1 = 2780000, B2 = 91760000 (P-1 stage 2)

B1 = 2780000 (P-1 stage 1)

B1 = 1837529 (P-1 stage 1)

B1 = 100000, B2 = 1675000 (P-1 stage 2)

B1 = 169860 (P-1 stage 1)

B1 = 134930 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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