M2109421 Mersenne number exponent details

Residue

Status

L-L

AC732D9824A26206

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	14.0863	67.1642%	140000	3010000	0.0283	3.1004%	14.1145	68.1822%	1.0180%
PrimeNet	2⁵⁸	0.0182	62.0690%	9000	160000	0.0016	2.6800%	0.0198	63.0855%	1.0166%
GPU72	2⁶²	0.2912	64.5161%	10000	140000	0.0016	1.4526%	0.2929	65.0316%	0.5154%
Difference	+5	+13.7950	+2.6481%	+130000	+2870000	+0.0266	+1.6478%	+13.8217	+3.1506%	+3.1506%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.0863

67.1642%

140000

3010000

0.0283

3.1004%

14.1145

68.1822%

1.0180%

PrimeNet

2⁵⁸

0.0182

62.0690%

9000

160000

0.0016

2.6800%

0.0198

63.0855%

1.0166%

GPU72

2⁶²

0.2912

64.5161%

10000

140000

0.0016

1.4526%

0.2929

65.0316%

0.5154%

Difference

+13.7950

+2.6481%

+130000

+2870000

+0.0266

+1.6478%

+13.8217

+3.1506%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2109421	4140204187393670550906679	25	81.776	981360332383547559 3 × 59 × 39694981 × 139675307	2016-05-29	39694981	139675307	285,382	4.3037	7.7019

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2109421

4140204187393670550906679

81.776

981360332383547559
3 × 59 × 39694981 × 139675307

2016-05-29

39694981

139675307

285,382

4.3037

7.7019

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.277%
2009-08-02T05:46:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	1.021%
2010-12-30T22:20:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.415%
2011-01-10T23:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.596%
2011-01-25T12:51:00	James Heinrich	Q6600	140000	3010000		-		-	-	0.028	-	-	3.100%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:05	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.055	-	-
2009-01-03T07:35:00	Sturle Sunde	ghia.ifi	2⁶⁰	2⁶¹		-	-	0.073	-	-
2012-03-30T07:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.146	-	-
2013-09-05T08:28:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.465	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.931	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.771	-	-
2015-12-27T16:49:18	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.543	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.043 GHz-days
Estimated T-Level:	1.200

Digits	B1	Curves	Complete	FacMiss
20	11000	24 / 100	0.240	78.568%
25	50000	24 / 280	0.086	91.772%

New Calculation Method

Total ECM effort:	2.043 GHz-days
Estimated T-Level:	1.200

Digits	B1	Complete	FacMiss
20	11000	0.774	46.108%
25	50000	0.070	93.242%
30	250000	0.004	99.570%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		21	1.788
50000	5000000	4140204187393670550906679	3	0.255

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-14T23:56:00	Luigi Morelli	AMD64x2	50000	5000000						3	0.255
2009-11-15T17:12:00	ANONYMOUS	fn-asterisk	50000	5000000						3	0.255
2011-06-26T13:21:00	S36049	Wolle5	50000	5000000						3	0.255
2013-04-09T11:10:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.255
2014-11-01T13:39:00	arnaud	srv-630	50000	5000000						3	0.255
2015-08-03T12:20:00	guru	w6	50000	5000000						3	0.255
2016-02-22T03:36:15	Bruce	Desk6	50000	5000000						3	0.255
2016-05-29T15:51:36	Bruce	Desk6	50000	5000000	4140204187393670550906679	81.776	3	2		3	0.255

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	ANONYMOUS	v4_computers	AC732D9824A26206	0.139

date

userid

compid

res64

spent (GHz-days)

1999-01-29T00:00:00

ANONYMOUS

v4_computers

AC732D9824A26206

0.139

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-07T03:31:59

Oliver Kruse

GTX-0

4140204187393670550906679

921CB04EF80FBB__

2017-11-17T09:53:16

kkmrkkblmbrbk

c4.xlarge

4140204187393670550906679

921CB04EF80FBB__

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 = 140000, B2 = 3010000 (P-1 stage 2)

B1 = 140000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 260000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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