M548423 Mersenne number exponent details

is 2 ⁵⁴⁸⁴²³ - 1

has 165092 decimal digits

takes 0.008 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	54.1807	70.1493%	15000000	1815000000	2.3909	12.1516%	56.5716	73.7766%	3.6273%
PrimeNet	2⁴⁰	0.0000	50.0000%	5500	190000	0.0003	19.7650%	0.0003	59.8825%	9.8825%
GPU72	2⁴⁴	0.0000	54.5455%	9000	320000	0.0005	14.8399%	0.0006	61.2909%	6.7454%
Difference	+23	+54.1807	+15.6038%	+14991000	+1814680000	+2.3904	-2.6883%	+56.5710	+12.4857%	+12.4857%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
548423	5216626769036150250652965673537	31	102.041	4756024792027458960194016 2⁵ × 3² × 7 × 17 × 367 × 739 × 101117 × 5060226793	2015-10-05	101117	5060226793	2.532e+11	5.8318	10.888

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-12-07T00:00:00	Alex Kruppa	v4_computers	100000	4000000		-		-	-	0.007	-	-	2.533%
2002-04-28T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.002	-	-	1.182%
2002-06-29T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.004	-	-	1.787%
2002-09-07T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.009	-	-	2.532%
2003-05-11T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.018	-	-	3.405%
2011-06-23T10:06:00	Jocelyn Larouche	Manual testing	400000	400000		-		-	-	0.008	-	-	1.501%
2011-06-26T19:18:00	Jocelyn Larouche	Manual testing	434354	434354		-		-	-	0.009	-	-	1.560%
2011-08-01T01:50:00	Jocelyn Larouche	Manual testing	723923	723923		-		-	-	0.015	-	-	1.951%
2012-07-14T15:56:00	Jocelyn Larouche	Manual testing	1096846	1096846		-		-	-	0.023	-	-	2.308%
2013-10-09T10:31:00	David Campeau	i5-2500k	1225000	37975000		-		-	-	0.068	-	-	5.757%
2015-10-05T20:08:08	mikr	Dell	1225000	37975000			5216626769036150250652965673537	31	102.041	0.068	0.016	0.136	5.757%
2021-08-19T05:28:28	ViliamF	3	15000000	1815000000		-		-	-	2.391	-	-	12.152%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-03-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁴		-	-	0.004	-	-
2022-03-07T08:27:02	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.004	-	-
2001-04-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.018	-	-
2002-01-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.035	-	-
2003-12-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.070	-	-
2022-03-07T08:27:02	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.210	-	-
2022-03-07T08:27:02	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	0.280	-	-
2015-07-10T21:07:00	NR	Manual testing	2⁶¹	2⁶²		-	-	0.560	-	-
2015-09-13T15:17:00	Gordon Spence	Manual testing	2⁶²	2⁶³		-	-	1.790	-	-
2015-09-13T15:17:00	Gordon Spence	Manual testing	2⁶³	2⁶⁴		-	-	3.580	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	16.152 GHz-days
Estimated T-Level:	26.125

Digits	B1	Curves	Complete	FacMiss
20	11000	424 / 100	4.240	1.410%
25	50000	424 / 280	1.514	21.937%
30	250000	144 / 640	0.225	79.838%

New Calculation Method

Total ECM effort:	16.152 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	21.032	0.000%
25	50000	2.551	7.798%
30	250000	0.238	78.858%
35	1000000	0.018	98.228%
40	3000000	0.001	99.887%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		280	4.523
250000	25000000		144	11.63

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-19T14:13:00	Chad Davis	Bayes	50000	5000000						1	0.016
2007-09-24T03:55:00	Chad Davis	Bayes	50000	5000000						1	0.016
2008-01-13T23:07:00	Team_Bundu	bundu1	50000	5000000						3	0.048
2008-08-03T17:02:00	Sturle Sunde	v17	50000	5000000						3	0.048
2008-10-20T20:41:00	Sturle Sunde	v21	50000	5000000						3	0.048
2009-01-14T20:21:00	Sturle Sunde	v22	50000	5000000						3	0.048
2009-02-26T00:42:00	Sturle Sunde	v21	50000	5000000						3	0.048
2009-04-08T05:38:00	S36049	Wolle3	50000	5000000						3	0.048
2009-07-01T05:03:00	Architects Cubed	m1_58	50000	5000000						3	0.048
2009-07-09T09:03:00	Architects Cubed	m1_73	50000	5000000						3	0.048
2009-08-07T22:38:00	Sturle Sunde	PREUSW40604NL	50000	5000000						3	0.048
2009-09-16T18:40:00	David Bessell	L301	50000	5000000						3	0.048
2009-10-11T17:12:00	JimBa	ISAserv	50000	5000000						3	0.048
2009-10-28T16:32:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2009-11-14T18:47:00	Sturle Sunde	FLB-ST-0033	50000	5000000						3	0.048
2009-12-04T06:47:00	Sturle Sunde	TOR-ST-0020	50000	5000000						3	0.048
2009-12-26T17:26:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2010-01-13T17:49:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2010-01-28T03:11:00	James Hintz	09_122109	50000	5000000						3	0.048
2010-02-09T05:45:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2010-03-01T07:46:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2010-03-22T16:13:00	Sturle Sunde	TOR-ST-0024	50000	5000000						3	0.048
2010-04-04T00:16:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2010-04-20T17:19:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2010-05-06T16:06:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2010-05-23T15:47:00	James Hintz	17_051310	50000	5000000						3	0.048
2010-06-12T02:23:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2010-07-03T20:58:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2010-07-31T03:44:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2010-08-24T01:41:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2010-09-09T02:16:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2010-09-25T00:53:00	Sturle Sunde	PREUSW40604NL	50000	5000000						3	0.048
2010-10-10T09:50:00	sannerud.com	Jim2010	50000	5000000						3	0.048
2010-10-23T17:32:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2010-11-06T05:03:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2010-11-24T21:10:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2010-12-06T18:38:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2010-12-19T04:33:00	Beat Bucheli	I7	50000	5000000						3	0.048
2011-01-06T01:14:00	Damian Silvestre	PcMa	50000	5000000						3	0.048
2011-01-18T18:06:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2011-01-31T16:01:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2011-02-15T18:58:00	Damian Silvestre	PcMa	50000	5000000						3	0.048
2011-02-26T22:18:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2011-03-12T02:06:00	Damian Silvestre	PcMa	50000	5000000						3	0.048
2011-03-22T19:49:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2011-04-09T17:21:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2011-04-29T03:56:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2011-05-17T02:02:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2011-05-30T22:21:00	Lukasz Wrobel	w-l	50000	5000000						3	0.048
2011-06-15T23:48:00	Sturle Sunde	PRE6S23JYHZD1NR	50000	5000000						3	0.048
2011-07-09T20:33:00	Lukasz Wrobel	w-l	50000	5000000						3	0.048
2011-08-04T12:19:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2011-09-04T22:04:00	Lukasz Wrobel	w-l	50000	5000000						3	0.048
2011-11-01T04:10:00	Sturle Sunde	PREUSW40604NL	50000	5000000						3	0.048
2011-12-16T23:11:00	ANONYMOUS	HYDRA	50000	5000000						3	0.048
2012-02-09T06:07:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2012-03-17T06:54:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.048
2012-05-28T23:06:00	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.048
2012-08-20T15:05:00	Lackó	Iroda_Laci_uj	50000	5000000						3	0.048
2012-10-01T21:50:00	Sturle Sunde	TOR-ST-0035	50000	5000000						3	0.048
2013-04-28T00:45:00	Sturle Sunde	PRECZB3140ZD8	50000	5000000						3	0.048
2013-11-28T04:20:00	Bruce	bfc-ws	50000	5000000						3	0.048
2014-01-23T23:15:00	dragon325	6005x64	50000	5000000						3	0.048
2014-03-30T14:06:00	Bruce	snowflake	50000	5000000						3	0.048
2014-04-02T08:22:00	Bruce	snowflake	50000	5000000						3	0.048
2014-07-11T07:01:00	Richard Otter	rjobio	50000	5000000						3	0.048
2015-04-12T08:53:00	Sergiosi	Manual testing	50000	5000000						86	1.389
2015-04-13T14:35:00	Sergiosi	Manual testing	250000	25000000						94	7.592
2020-12-11T12:22:40	TJAOI	Manual testing	250000	25000000						50	4.038

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2001-08-18T00:00:00	ANONYMOUS	v4_computers	2D6DC68DE6E93439	0.008
2015-04-11T07:44:00	MadPoo	Manual testing	2D6DC68DE6E93439	0.008

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T10:43:41

Oliver Kruse

GTX-2

5216626769036150250652965673537

7A483B76167BA8__

2017-09-28T09:43:04

Oliver Kruse

Manual testing

5216626769036150250652965673537

7A483B76167BA8__

2017-11-07T05:04:28

kkmrkkblmbrbk

c4.xlarge

5216626769036150250652965673537

7A483B76167BA8__

2020-04-19T05:55:01

Oliver Kruse

AddPrpType5

5216626769036150250652965673537

106D736136DC00__

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 = 15000000, B2 = 1815000000 (P-1 stage 2)

B1 = 15000000 (P-1 stage 1)

B1 = 1225000, B2 = 37975000 (P-1 stage 2)

B1 = 1225000 (P-1 stage 1)

B1 = 1096846 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 723923 (P-1 stage 1)

B1 = 434354 (P-1 stage 1)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 400000 (P-1 stage 1)

B1 = 100000, B2 = 4000000 (P-1 stage 2)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

B1 = 16384 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁷

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁴

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

Last modified: 2022-03-07T08:27:02+00:00

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