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2009-05-17, 15:29   #12
10metreh

Nov 2008

1001000100102 Posts

Quote:
 Originally Posted by Andi47 The status of "reserved", "available" and "terminated" is color-coded: yellow for reserved and light blue for available. The Lehmer Five are saying "last editor: P. Zimmermann", but they are color-coded in light blue (meaning "available"). I checked with firefox and IE.
Ah, I see now.

 2009-05-17, 19:53 #13 kar_bon     Mar 2006 Germany 2×3×11×43 Posts i updated the Lehmer 5 reserved by P.Zimmermann (and 4788 and 130396). the data i got was out of date and i was not sure if he works on it further. need some time to make all things work/look fine because i'm not so familiar with drivers/guides or the current reservations (only out of this forum so far). please post here, if there're any other errors. attached a view of that page it should look like this. if not there's something not correct with the browser settings. Attached Thumbnails   Last fiddled with by kar_bon on 2009-05-17 at 19:57
2009-05-18, 03:01   #14
schickel

"Frank <^>"
Dec 2004
CDP Janesville

212210 Posts

Quote:
 Originally Posted by kar_bon i updated the Lehmer 5 reserved by P.Zimmermann (and 4788 and 130396). the data i got was out of date and i was not sure if he works on it further.
I think they're currently low priority. If there were the interest, the forum could adopt them, too.
Quote:
 need some time to make all things work/look fine because i'm not so familiar with drivers/guides or the current reservations (only out of this forum so far).
Did you check the wiki article? It covers the main points about the drivers; just ask here if you have any questions.....

As far as reservations, to the best of my knowledge, we're alone in the field in the 100-200k range. Check this thread for the status of other ranges.....
Quote:
 please post here, if there're any other errors.
I didn't see anything right off hand. Nice work on the table.....
Quote:
 attached a view of that page it should look like this. if not there's something not correct with the browser settings.

 2009-05-18, 17:12 #15 10metreh     Nov 2008 44228 Posts Errrm... 2^2*7 is not the downdriver.
 2009-05-20, 04:48 #16 schickel     "Frank <^>" Dec 2004 CDP Janesville 2·1,061 Posts Couple of things 4788 - 27 * 32 is a guide, not a driver. 29772 - 24 * 7 is a guide. 103296 - 22 * 3 is a guide. 112638 - 22 * 32 is a guide 115302 - 26 * 3 is actually controlled by 26 * 127 139314 - 25 * 7 is a guide. 150096 - 24 * 3 is a guide. 162126 - 22 * 32 * 5 is a guide.
2009-05-20, 05:32   #17
axn

Jun 2003

2×32×7×37 Posts

Quote:
 Originally Posted by schickel 4788 - 27 * 32 is a guide, not a driver.
Hmmm... Either my definition of guide is messed up or most of these are incorrect. What's the definition of driver/guide you're using?

Code:
  4788  2^7*3^2*17 Guide
9708  2^2*7  Driver
10212  2*3    Driver
29772  2^4    Guide
88662  2^2    Guide
100320  2^2*7  Guide
100436  2^4*31 Guide
103296  2^2    Guide
112638  2^2    Guide
115302  2^6*127 Driver
123960  2^2    Guide
128370  2^2    Guide
129336  2^2    Guide
132792  2^4*31 Driver
132920  2^4*31 Driver
139314  2^5*7  Guide
145008  2*3    Driver
149808  2^2*7  Driver
150096  2^4    Guide
162126  2^2    Guide
167148  2^4    Guide
168912  2^4    Guide
171018  2^2    Guide
175410  2*3^2  Driver
182224  2^4*31 Driver

2009-05-20, 05:52   #18
schickel

"Frank <^>"
Dec 2004
CDP Janesville

2×1,061 Posts

Quote:
 Originally Posted by axn Hmmm... Either my definition of guide is messed up or most of these are incorrect. What's the definition of driver/guide you're using?
Quote:
 R. K. GUY and J. L. SELFRIDGE, "What drives an aliquot sequence," Math. of Comp. v. 29, n. 129, 1975, pp. 101-107.
I'm not sure if my use of guide is correct, but I use "guide" for anything that persists, but that's not a driver.

The drivers outlined in the above article are:
Code:
$2$ (the downdriver)

$2^2 * 7$

$2^3 * 3$

$2^3 * 3 * 5$

$2^4 * 31$

$2^5 * 3 * 7$

$2^6 * 127$

$2^9 * 3 * 11 * 31$

Last fiddled with by schickel on 2009-05-20 at 05:56

2009-05-20, 06:25   #19
10metreh

Nov 2008

91216 Posts

Quote:
 Originally Posted by schickel but I use "guide" for anything that persists, but that's not a driver.
What is the word Guy and Selfridge suggest using for things like 2^2*3, which would be classified as having the "guide" 2^2 (seems completely mad)?

Last fiddled with by 10metreh on 2009-05-20 at 06:25

2009-05-20, 06:47   #20
schickel

"Frank <^>"
Dec 2004
CDP Janesville

212210 Posts

Quote:
 Originally Posted by 10metreh What is the word Guy and Selfridge suggest using for things like 2^2*3, which would be classified as having the "guide" 2^2 (seems completely mad)?
Here's the definition from the article:
Quote:
 Originally Posted by Guy&Selfridge Define a guide to be $2^a$, together with a subset of the prime factors of $\ \sigma(2^a)$. A driver is defined as a number $\ 2^av$ with $\ a>0$, $v$ odd, $v|\sigma(2^a)$ and $2^{a-1}|\sigma(v)$. The last requirement is included so that the power of the prime 2 will tend to persist at least as well as it does for the driver 2 itself, for which the condition is trivially satisfied.
Further down, they give these as guides:
Code:
$2^2$

$2^3$

$2^35$

$2^4$

$2^53$

$2^57$
So, I have been a little, um, imprecise, in calling, for example, $2^23$, a guide. The guide is actually $2^2$...

And I actually have been lax: the drivers include the even perfect numbers.....

2009-05-20, 06:57   #21
axn

Jun 2003

2×32×7×37 Posts

Quote:
 Originally Posted by schickel Drivers are defined in this article:I'm not sure if my use of guide is correct, but I use "guide" for anything that persists, but that's not a driver.
Ok. I get one definition of guide from here (PDF file).

Basically, what forms a driver or guide depends on the factorisation of Sigma(2^a).

EDIT:- Frank was here first :)

Last fiddled with by axn on 2009-05-20 at 06:58

2009-05-20, 07:07   #22
schickel

"Frank <^>"
Dec 2004
CDP Janesville

1000010010102 Posts

Quote:
 Originally Posted by axn Ok. I get one definition of guide from here (PDF file). Basically, what forms a driver or guide depends on the factorisation of Sigma(2^a). EDIT:- Frank was here first :)
Yes, in the 3630 article, they give a quick review of the definition. If you're interested in the full proof, you have to go back to the Guy & Selfridge article.

If you have access to a library with inter-library loan privileges with a school, you can request a copy of the original article. (I got mine from a co-worker who was moonlighting from their day job at the local community college....)

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