M1398541 Mersenne number exponent details

Residue

Status

L-L

43466DD68B1C4BCF

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	21.2464	68.6567%	3106900	111849000	0.5000	8.2304%	21.7464	71.2364%	2.5797%
PrimeNet	2⁵⁶	0.0069	62.5000%	6500	110000	0.0007	2.7616%	0.0075	63.5356%	1.0356%
GPU72	2⁶⁰	0.1098	65.0000%	6000	65000	0.0005	1.2121%	0.1103	65.4242%	0.4242%
Difference	+7	+21.1365	+3.6567%	+3100900	+111784000	+0.4995	+7.0183%	+21.6360	+5.8122%	+5.8122%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

21.2464

68.6567%

3106900

111849000

0.5000

8.2304%

21.7464

71.2364%

2.5797%

PrimeNet

2⁵⁶

0.0069

62.5000%

6500

110000

0.0007

2.7616%

0.0075

63.5356%

1.0356%

GPU72

2⁶⁰

0.1098

65.0000%

6000

65000

0.0005

1.2121%

0.1103

65.4242%

0.4242%

Difference

+21.1365

+3.6567%

+3100900

+111784000

+0.4995

+7.0183%

+21.6360

+5.8122%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1398541	409000814702658074534959463	27	88.402	146224105944215462591 17 × 1297 × 1439 × 345547 × 13337123	2014-10-05	345547	13337123	78,109,239	0.0583	0.0751

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1398541

409000814702658074534959463

88.402

146224105944215462591
17 × 1297 × 1439 × 345547 × 13337123

2014-10-05

345547

13337123

78,109,239

0.0583

0.0751

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-04-14T00:00:00	Jocelyn Larouche	v4_computers	20000	295000		-		-	-	0.002	-	-	0.979%
2014-04-16T21:17:00	Jocelyn Larouche	Manual testing	110000	110000		-		-	-	0.006	-	-	0.900%
2014-04-17T21:12:00	Jocelyn Larouche	Manual testing	120000	120000		-		-	-	0.007	-	-	0.946%
2014-04-23T21:11:00	ANONYMOUS	Manual testing	200000	200000		-		-	-	0.011	-	-	1.246%
2014-10-05T04:29:00	mikr	MSI	3106900	111849000	12		409000814702658074534959463	27	88.402	0.500	0.107	1.000	8.230%
2016-03-17T19:13:47	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 409000814702658074534959463	-	-	0.071	-	-	4.907%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-10-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.014	-	-
2003-07-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.027	-	-
2022-03-07T17:32:41	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.082	-	-
2009-02-15T10:37:00	Sturle Sunde	gibus.ifi	2⁶⁰	2⁶¹		-	-	0.110	-	-
2012-07-05T14:35:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.220	-	-
2013-01-27T10:10:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.702	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.362 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.362 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.357	25.749%
30	250000	0.113	89.315%
35	1000000	0.008	99.236%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	11.81
250000	35000000		50	13.55

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-12-31T14:20:00	Steve Scott	Epox	50000	5000000						1	0.047
2008-12-07T23:28:00	Luigi Morelli	AMD64x2	50000	5000000						3	0.141
2009-05-21T01:39:00	Lukasz Wrobel	UNIX_05	50000	5000000						3	0.141
2009-08-21T10:32:00	Lukasz Wrobel	WORKER-1	50000	5000000						3	0.141
2009-12-26T20:52:00	sannerud.com	snap1	50000	5000000						3	0.141
2010-10-05T14:17:00	Kamil_Górski	thefault	50000	5000000						3	0.141
2011-08-21T10:48:00	Kamil_Górski	thefault	50000	5000000						3	0.141
2012-05-17T10:42:00	James Hintz	chris3	50000	5000000						3	0.141
2012-11-28T23:53:00	Salvetay	server5	50000	5000000						3	0.141
2013-10-16T19:24:00	OS1	Tina	50000	5000000						3	0.141
2014-03-02T09:06:00	Bruce	snowflake	50000	5000000						3	0.141
2014-04-24T02:19:00	OS1	Tina	50000	5000000						3	0.141
2018-12-07T13:07:43	TJAOI	Manual testing	50000	5000000						217	10.21
2021-11-11T10:31:47	TJAOI	Manual testing	250000	35000000						50	13.55

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 = 3106900, B2 = 111849000 (P-1 stage 2)

B1 = 3106900 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 120000 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

B1 = 20000, B2 = 295000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

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