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10metreh 2009-05-17 15:29

[quote=Andi47;173902]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.[/quote]

Ah, I see now. :smile:

kar_bon 2009-05-17 19:53

1 Attachment(s)
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the data i got was out of date and i was not sure if he works on it further.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.

schickel 2009-05-18 03:01

[QUOTE=kar_bon;173926]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the data i got was out of date and i was not sure if he works on it further.[/QUOTE]I think they're currently low priority.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).[/quote]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 [url="http://www.mersenneforum.org/showthread.php?t=11625"]thread[/url] for the status of other ranges.....[quote]please post here, if there're any other errors.[/quote]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.[/QUOTE]

10metreh 2009-05-18 17:12

Errrm... 2^2*7 is not the downdriver.

schickel 2009-05-20 04:48

Couple of things
 
[b]4788 - 2[sup]7[/sup] * 3[sup]2[/sup][/b] is a guide, not a driver.

[b]29772 - 2[SUP]4[/SUP] * 7[/b] is a guide.

[b]103296 - 2[SUP]2[/SUP] * 3[/b] is a guide.

[b]112638 - 2[SUP]2[/SUP] * 3[SUP]2[/SUP][/b] is a guide

[b]115302 - 2[SUP]6[/SUP] * 3[/b] is actually controlled by [b]2[SUP]6[/SUP] * 127[/b]

[b]139314 - 2[SUP]5[/SUP] * 7[/b] is a guide.

[b]150096 - 2[SUP]4[/SUP] * 3[/b] is a guide.

[b]162126 - 2[SUP]2[/SUP] * 3[SUP]2[/SUP] * 5[/b] is a guide.

axn 2009-05-20 05:32

[QUOTE=schickel;174242][b]4788 - 2[sup]7[/sup] * 3[sup]2[/sup][/b] is a guide, not a driver.
<snip>[/QUOTE]

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
[/code]

schickel 2009-05-20 05:52

[QUOTE=axn;174247]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]Drivers are defined in this article:[quote]R. K. GUY and J. L. SELFRIDGE, "What drives an aliquot sequence," Math. of Comp. v. 29, n. 129, 1975, pp. 101-107.[/quote]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][tex]2[/tex] (the downdriver)

[tex]2^2 * 7[/tex]

[TEX]2^3 * 3[/TEX]

[TEX]2^3 * 3 * 5[/TEX]

[TEX]2^4 * 31[/TEX]

[TEX]2^5 * 3 * 7[/TEX]

[TEX]2^6 * 127[/TEX]

[TEX]2^9 * 3 * 11 * 31[/TEX][/code]

10metreh 2009-05-20 06:25

[quote=schickel;174250]but I use "guide" for anything that persists, but that's not a driver.[/quote]

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)?

schickel 2009-05-20 06:47

[QUOTE=10metreh;174256]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)?[/QUOTE]Here's the definition from the article:[quote=Guy&Selfridge]Define a [U]guide[/U] to be [tex]2^a[/tex], together with a subset of the prime factors of [TEX]\ \sigma(2^a)[/TEX]. A [U]driver[/U] is defined as a number [TEX]\ 2^av[/TEX] with [TEX]\ a>0[/TEX], [TEX]v[/TEX] odd, [TEX]v|\sigma(2^a)[/TEX] and [TEX]2^{a-1}|\sigma(v)[/TEX]. 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.[/quote]Further down, they give these as guides:[code][TEX]2^2[/TEX]

[TEX]2^3[/TEX]

[TEX]2^35[/TEX]

[TEX]2^4[/TEX]

[TEX]2^53[/TEX]

[TEX]2^57[/TEX]
[/code]So, I have been a little, um, imprecise, in calling, for example, [TEX]2^23[/TEX], a guide. The guide is actually [TEX]2^2[/TEX]...

And I actually have been lax: the drivers include the [i]even perfect numbers[/i].....

axn 2009-05-20 06:57

[QUOTE=schickel;174250]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.
[/QUOTE]

Ok. I get one definition of guide from [URL="http://www.emis.de/journals/EM/expmath/volumes/11/11.2/3630finishes1.pdf"]here[/URL] (PDF file).

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

EDIT:- Frank was here first :)

schickel 2009-05-20 07:07

[QUOTE=axn;174265]Ok. I get one definition of guide from [URL="http://www.emis.de/journals/EM/expmath/volumes/11/11.2/3630finishes1.pdf"]here[/URL] (PDF file).

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

EDIT:- Frank was here first :)[/QUOTE]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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