M1653287 Mersenne number exponent details

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M1653287

<<<

>>>

is 2 ^1653287 - 1

has 497689 decimal digits

takes 0.078 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	7E1185BBD8DD4CAA	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	17.9726	68.6567%	8000000	400000000	2.0034	10.6535%	19.9760	71.9959%	3.3392%
PrimeNet	2⁵⁷	0.0116	63.1579%	7000	120000	0.0009	2.5644%	0.0125	64.1027%	0.9448%
GPU72	2⁶¹	0.1858	65.5738%	7000	70000	0.0007	1.1516%	0.1865	65.9702%	0.3964%
Difference	+6	+17.7868	+3.0829%	+7993000	+399930000	+2.0026	+9.5019%	+19.7895	+6.0256%	+6.0256%

Known prime factors (1 factor, 95.4 bits, 0.00577005% 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
1653287	52105858867240908247112178769	29	95.395	15758261834527492276632 2³ × 3 × 79 × 1579 × 1811 × 15493 × 187600451	2018-08-12	15493	187600451	9.404e+9	0.6985	1.3027

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2012-02-29T17:08:00	Axon	Manual testing	100000	100000		-		-	-	0.007	-	-	0.878%
2012-02-29T17:12:00	Axon	Manual testing	200000	200000		-		-	-	0.014	-	-	1.282%
2012-02-29T18:09:00	Axon	Manual testing	300000	300000		-		-	-	0.020	-	-	1.563%
2012-02-29T18:12:00	Axon	Manual testing	400000	400000		-		-	-	0.027	-	-	1.783%
2012-02-29T19:09:00	Axon	Manual testing	500000	500000		-		-	-	0.034	-	-	1.965%
2012-02-29T19:12:00	Axon	Manual testing	600000	600000		-		-	-	0.041	-	-	2.121%
2012-02-29T20:08:00	Axon	Manual testing	700000	700000		-		-	-	0.048	-	-	2.259%
2012-02-29T20:11:00	Axon	Manual testing	800000	800000		-		-	-	0.055	-	-	2.382%
2012-02-29T21:09:00	Axon	Manual testing	900000	900000		-		-	-	0.061	-	-	2.493%
2012-02-29T21:13:00	Axon	Manual testing	1000000	1000000		-		-	-	0.068	-	-	2.595%
2012-03-01T06:08:00	Axon	Manual testing	1000000	8000000		-		-	-	0.094	-	-	4.724%
2012-03-01T07:09:00	Axon	Manual testing	1000000	20000000		-		-	-	0.139	-	-	5.689%
2017-12-24T12:25:08	Jocelyn Larouche	low 4M	2000000	20000000	12	-		-	-	0.203	-	-	6.015%
2018-02-08T12:52:28	Jocelyn Larouche	low 4M	1653287	20000000	12	-		-	-	0.181	-	-	5.935%
2018-02-08T17:39:28	Jocelyn Larouche	low 4M	1653287	40000000	12	-		-	-	0.255	-	-	6.738%
2018-02-18T02:59:34	Jocelyn Larouche	low 4M	1653287	80000000	12	-		-	-	0.404	-	-	7.549%
2018-03-30T19:42:34	Jocelyn Larouche	low 4M	1653287	165328700	12	-		-	-	0.721	-	-	8.404%
2018-08-12T10:05:53	mikr	S053	8000000	400000000	12		52105858867240908247112178769	29	95.395	2.003	0.156	4.007	10.653%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-12-04T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.006	-	-
1997-12-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.006	-	-
1998-02-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.006	-	-
1999-07-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
2003-05-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.023	-	-
2016-02-23T16:28:44	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.070	-	-
2010-04-29T03:30:00	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.093	-	-
2016-02-23T16:28:44	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.186	-	-
2010-08-13T02:23:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.965	-	-
2016-02-23T16:28:44	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.594	-	-
2015-05-08T01:31:00	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.188	-	-
2015-05-08T17:30:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	2.260	-	-
2015-10-11T16:52:50	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.520	-	-
2017-10-20T14:50:27	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	9.040	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	16.595 GHz-days
Estimated T-Level:	25.000

Digits	B1	Curves	Complete	FacMiss
20	11000	280 / 100	2.800	5.996%
25	50000	280 / 280	1.000	36.722%

New Calculation Method

Total ECM effort:	16.595 GHz-days
Estimated T-Level:	25.000

Digits	B1	Complete	FacMiss
20	11000	9.032	0.012%
25	50000	0.816	44.205%
30	250000	0.050	95.097%
35	1000000	0.002	99.770%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		280	16.60

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-05-25T09:01:00	arnaud	SPR15	50000	5000000						3	0.178
2009-06-08T21:44:00	James Hintz	08_060209	50000	5000000						3	0.178
2010-05-25T15:11:00	spaz	clausewitz	50000	5000000						3	0.178
2011-09-30T15:56:00	S36049	Wolle5	50000	5000000						3	0.178
2013-03-14T15:25:00	Donna Noble	opt4820	50000	5000000						3	0.178
2013-11-30T02:29:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-07-24T03:13:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-09-20T19:53:00	mikr	MSI	50000	5000000						12	0.711
2016-05-16T09:30:00	Bruce	DESK3	50000	5000000						3	0.178
2016-08-09T23:51:37	Bruce	DESK3	50000	5000000						3	0.178
2016-10-12T20:00:46	Bruce	DESK3	50000	5000000						3	0.178
2016-12-09T23:13:44	Bruce	DESK3	50000	5000000						3	0.178
2017-02-02T02:56:16	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2017-08-28T11:07:38	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2017-12-19T21:37:58	Bruce	DESK3	50000	5000000						3	0.178
2018-02-13T13:36:57	Lelikoid	QH	50000	5000000						3	0.178
2018-04-24T14:55:37	Lelikoid	QH	50000	5000000						3	0.178
2018-05-09T14:34:56	VictordeHollander	Manual testing	50000	5000000						220	13.04

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-12-04T00:00:00	ANONYMOUS	v4_computers	7E1185BBD8DD4CAA	0.078
1997-12-21T00:00:00	ANONYMOUS	v4_computers	7E1185BBD8DD4CAA	0.078
1998-02-01T00:00:00	ANONYMOUS	v4_computers	7E1185BBD8DD4CAA	0.078
2015-11-13T16:44:28	MadPoo	Manual testing	7E1185BBD8DD4CAA	0.078

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-08-12T10:41:03

ATH

ec2-PRPCF

52105858867240908247112178769

9E78360A467E97__

2018-08-14T10:14:51

Ruzovej

Ondra_Ntb

52105858867240908247112178769

9E78360A467E97__

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 = 8000000, B2 = 400000000 (P-1 stage 2)

B1 = 1653287, B2 = 165328700 (P-1 stage 2)

B1 = 8000000 (P-1 stage 1)

B1 = 1653287, B2 = 80000000 (P-1 stage 2)

B1 = 1653287, B2 = 40000000 (P-1 stage 2)

B1 = 2000000, B2 = 20000000 (P-1 stage 2)

B1 = 1653287, B2 = 20000000 (P-1 stage 2)

B1 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 1653287 (P-1 stage 1)

B1 = 1000000, B2 = 8000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 900000 (P-1 stage 1)

B1 = 800000 (P-1 stage 1)

B1 = 700000 (P-1 stage 1)

B1 = 600000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 400000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2018-08-14T10:14:51+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