M1821821 Mersenne number exponent details

Residue

Status

L-L

CB31EB82C84359A2

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	16.3100	68.6567%	2780000	91760000	0.6000	8.1257%	16.9100	71.2036%	2.5469%
PrimeNet	2⁵⁷	0.0105	63.1579%	8000	150000	0.0012	2.8767%	0.0118	64.2177%	1.0598%
GPU72	2⁶¹	0.1686	65.5738%	9000	130000	0.0012	1.5582%	0.1698	66.1102%	0.5364%
Difference	+6	+16.1414	+3.0829%	+2771000	+91630000	+0.5988	+6.5675%	+16.7402	+5.0934%	+5.0934%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.3100

68.6567%

2780000

91760000

0.6000

8.1257%

16.9100

71.2036%

2.5469%

PrimeNet

2⁵⁷

0.0105

63.1579%

8000

150000

0.0012

2.8767%

0.0118

64.2177%

1.0598%

GPU72

2⁶¹

0.1686

65.5738%

9000

130000

0.0012

1.5582%

0.1698

66.1102%

0.5364%

Difference

+16.1414

+3.0829%

+2771000

+91630000

+0.5988

+6.5675%

+16.7402

+5.0934%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1821821	2953620920993753590103	22	71.323	810623250306631 810623250306631	2021-04-09	1	810623250306631	380.10	3,474,129	6,488,705
1821821	41450530895203527765583	23	75.134	11376126110963571 3 × 3792042036987857	2016-08-27	3	3792042036987857	4,301.1	16,251,744	30,353,732

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1821821

2953620920993753590103

71.323

810623250306631
810623250306631

2021-04-09

810623250306631

380.10

3,474,129

6,488,705

1821821

41450530895203527765583

75.134

11376126110963571
3 × 3792042036987857

2016-08-27

3792042036987857

4,301.1

16,251,744

30,353,732

exponent	prime factors	composite factor	digits	bits*
1821821	2953620920993753590103 41450530895203527765583	122429155238371081155010628976278748052825049	45	146.457

exponent

prime factors

composite factor

digits

bits*

1821821

2953620920993753590103
41450530895203527765583

122429155238371081155010628976278748052825049

146.457

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-10-02T06:40:00	harlee	P4_2600	100000	1675000		-		-	-	0.015	-	-	2.490%
2014-05-19T21:00:00	Jocelyn Larouche	Manual testing	135231	135231		-		-	-	0.011	-	-	1.060%
2014-09-22T21:00:00	Jocelyn Larouche	Manual testing	170462	170462		-		-	-	0.013	-	-	1.200%
2015-06-02T21:26:00	mikr	MSI	2780000	91760000		-		-	-	0.600	-	-	8.126%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:28:53	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.084	-	-
2010-04-10T15:57:00	Architects Cubed	Manual testing	2⁶⁰	2⁶¹		-	-	0.084	-	-
2016-02-23T16:28:53	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.169	-	-
2011-03-08T05:14:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.876	-	-
2016-02-23T16:28:53	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.539	-	-
2015-04-25T06:39:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.078	-	-
2015-04-25T06:39:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.051	-	-
2015-09-03T11:06:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.102	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.216 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:	19.216 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.575	0.019%
25	50000	0.777	45.986%
30	250000	0.048	95.308%
35	1000000	0.002	99.779%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	2.278
50000	5000000	41450530895203527765583	3	0.207
50000	6600000		102	7.937
50000	6600000	2953620920993753590103	113	8.793

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-09-25T22:09:00	Sturle Sunde	jobbtest	50000	5000000						3	0.207
2009-10-14T01:18:00	SubPrime	abd0	50000	5000000						3	0.207
2010-11-03T22:58:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.207
2012-05-09T14:06:00	OS1	L3	50000	5000000						3	0.207
2013-08-03T12:39:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-04-23T03:31:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-09-21T19:05:00	mikr	MSI	50000	5000000						12	0.828
2016-05-25T12:17:24	Bruce	DESK3	50000	5000000						3	0.207
2016-08-27T13:15:37	Bruce	DESK3	50000	5000000	41450530895203527765583	75.134	3	2		3	0.207
2021-04-09T16:11:54	TJAOI	Manual testing	50000	6600000	2953620920993753590103	71.323	113	2		113	8.793
2021-04-09T16:11:55	TJAOI	Manual testing	50000	6600000						102	7.937

date	userid	compid	res64	spent (GHz-days)
1999-01-10T00:00:00	ANONYMOUS	v4_computers	CB31EB82C84359A2	0.099
2015-07-04T19:28:00	MadPoo	Manual testing	CB31EB82C84359A2	0.099

date

userid

compid

res64

spent (GHz-days)

1999-01-10T00:00:00

ANONYMOUS

v4_computers

CB31EB82C84359A2

0.099

2015-07-04T19:28:00

MadPoo

Manual testing

CB31EB82C84359A2

0.099

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T23:33:07

Oliver Kruse

GTX-1

41450530895203527765583

A8FC3796932FAF__

2017-11-06T01:04:26

ATH

ec2-1xf

41450530895203527765583

A8FC3796932FAF__

2021-04-10T12:06:23

XZT

N4640G1

2953620920993753590103

41450530895203527765583

D9B294CCE60D1FA2

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

B1 = 2780000 (P-1 stage 1)

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

B1 = 170462 (P-1 stage 1)

B1 = 135231 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

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