M1473301 Mersenne number exponent details

≡

M1473301

<<<

>>>

is 2 ^1473301 - 1

has 443508 decimal digits

takes 0.056 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	850D9F439C861155	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	20.1683	68.6567%	2000000	60000000	0.2857	7.2410%	20.4539	70.9263%	2.2696%
PrimeNet	2⁵⁶	0.0065	62.5000%	7000	120000	0.0007	2.9130%	0.0072	63.5924%	1.0924%
GPU72	2⁶⁰	0.1042	65.0000%	6500	100000	0.0006	1.4478%	0.1049	65.5067%	0.5067%
Difference	+7	+20.0640	+3.6567%	+1993500	+59900000	+0.2850	+5.7932%	+20.3490	+5.4195%	+5.4195%

Known prime factors (1 factor, 82.1 bits, 0.00557267% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1473301	5190910929292951154709817	25	82.102	1761660016959518508 2² × 3 × 7 × 20972143059041887	2016-02-03	7	20972143059041887	1,172,485	63,257,518	118,147,427

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-29T00:00:00	Team Prime Rib	v4_computers	20000	270000		-		-	-	0.002	-	-	0.962%
2010-10-22T12:52:00	Rob_Dee	twopc	100000	200000		-		-	-	0.006	-	-	1.219%
2010-10-23T12:42:00	Rob_Dee	twopc	200000	300000		-		-	-	0.011	-	-	1.523%
2010-10-24T12:50:00	Rob_Dee	twopc	200000	1000000		-		-	-	0.013	-	-	2.338%
2010-10-25T12:25:00	Rob_Dee	twopc	200000	2000000		-		-	-	0.017	-	-	2.826%
2010-10-26T10:50:00	Rob_Dee	twopc	200000	3000000		-		-	-	0.020	-	-	3.118%
2010-10-27T12:43:00	Rob_Dee	twopc	200000	4000000		-		-	-	0.023	-	-	3.328%
2010-10-28T11:45:00	Rob_Dee	twopc	200000	5000000		-		-	-	0.026	-	-	3.492%
2014-11-19T23:20:00	Jocelyn Larouche	Manual testing	243565	243565		-		-	-	0.013	-	-	1.388%
2015-01-26T12:23:00	Jocelyn Larouche	Manual testing	294713	294713		-		-	-	0.016	-	-	1.522%
2015-01-28T21:36:00	Jocelyn Larouche	Manual testing	324184	324184		-		-	-	0.018	-	-	1.591%
2015-01-31T14:55:00	Jocelyn Larouche	Manual testing	356602	356602		-		-	-	0.020	-	-	1.663%
2015-02-15T21:12:00	Jocelyn Larouche	Manual testing	392262	392262		-		-	-	0.022	-	-	1.736%
2015-02-20T16:56:00	Jocelyn Larouche	Manual testing	431488	431488		-		-	-	0.024	-	-	1.811%
2015-02-26T11:47:00	alpertron	Manual testing	2000000	60000000		-		-	-	0.286	-	-	7.241%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-05-20T00:00:00	Jocelyn Larouche	v4_computers	2¹	2⁵⁷		-	-	0.013	-	-
2003-07-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.026	-	-
2016-02-23T16:28:34	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.078	-	-
2010-05-08T19:20:00	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.104	-	-
2016-02-23T16:28:34	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.208	-	-
2011-04-05T20:59:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	1.083	-	-
2016-02-23T16:28:34	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.666	-	-
2015-04-03T01:54:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.333	-	-
2015-04-03T01:54:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.536	-	-
2015-09-21T11:27:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	5.072	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	11.916 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:	11.916 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		249	11.82
50000	5000000	5190910929292951154709817	2	0.095

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-01-09T04:42:00	Steve Scott	Abit	50000	5000000						3	0.142
2009-03-07T21:59:00	Sturle Sunde	FLB-ST-0038	50000	5000000						3	0.142
2009-11-08T18:29:00	JimBa	NASsrvr	50000	5000000						3	0.142
2011-04-09T17:48:00	Lupo	yorick	50000	5000000						3	0.142
2012-08-26T03:09:00	Bud	annan	50000	5000000						3	0.142
2013-06-01T14:59:00	Sara	Sara	50000	5000000						3	0.142
2014-01-07T07:36:00	AdolfNor	X2	50000	5000000						3	0.142
2014-08-14T13:16:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2015-03-25T14:48:00	codest	aliyun	50000	5000000						3	0.142
2015-10-19T19:20:58	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2016-02-03T03:24:31	Chang Chia-Tche	exbpc13	50000	5000000	5190910929292951154709817	82.102	2	2		2	0.095
2019-04-19T08:39:09	TJAOI	Manual testing	50000	5000000						219	10.40

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-11-28T00:00:00	ANONYMOUS	v4_computers	850D9F439C861155	0.056
2015-07-01T17:35:00	MadPoo	Manual testing	850D9F439C861155	0.056

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T05:04:19

Oliver Kruse

GTX-2

5190910929292951154709817

41033623493A0F__

2017-10-28T06:36:55

kkmrkkblmbrbk

c4.xlarge

5190910929292951154709817

41033623493A0F__

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 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 200000, B2 = 5000000 (P-1 stage 2)

B1 = 431488 (P-1 stage 1)

B1 = 200000, B2 = 4000000 (P-1 stage 2)

B1 = 392262 (P-1 stage 1)

B1 = 356602 (P-1 stage 1)

B1 = 200000, B2 = 3000000 (P-1 stage 2)

B1 = 324184 (P-1 stage 1)

B1 = 200000, B2 = 2000000 (P-1 stage 2)

B1 = 294713 (P-1 stage 1)

B1 = 200000, B2 = 1000000 (P-1 stage 2)

B1 = 243565 (P-1 stage 1)

B1 = 200000, B2 = 300000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 100000, B2 = 200000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 20000, B2 = 270000 (P-1 stage 2)

B1 = 20000 (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

10¹⁷

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2019-04-19T08:39:09+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