Wikipedia talk:WikiProject Numbers/Archive 2

Possible Wikipedia discovery

It looks to me like Wikipedia may have discovered an intersting mathematical property: centered hexagonal numbers that are prime are Cuban primes. If Wikipedia has indeed discovered this, it will be one fact giving tremendous validation to doing articles on individual numbers. Numerao 22:45, 15 Mar 2004 (UTC)

That's fascinating, I too noticed it. But I have a feeling this has already been discovered. It's too difficult these days to make mathematical discoveries without the aid of advanced mathematics, such as calculus. But even if this was a Wikipedia-enabled discovery, I doubt it would silence the fanatic deletionists. They would scream "Wikipedia is not research!" PrimeFan 20:32, 16 Mar 2004 (UTC)

Actually, the explanation for this is fairly simple. The cuban primes are primes of the form (x³-y³)/(x-y). When x = n+1 and y=n, then this is ((n+1)³-n³)/((n+1)-n), which simplifies to 3n²+3n+1. And that's exactly the general form of a centered hexagonal number. So it's bound to be already noticed, if not well-known. 4pq1injbok 16:08, 12 Jul 2004 (UTC)

Of course! Thank you very much for that explanation, 4pq1injbok. Perhaps we should mention this in the respective articles. PrimeFan 22:08, 12 Jul 2004 (UTC)

I've added a few words to this effect to each. 4pq1injbok 04:50, 14 Jul 2004 (UTC)

Msg for the talk pages?

Maybe we should add to talk pages of articles a short link to WikiProject Numbers, or a message "Template:NumberTalk" similar to Template:BirdTalk or Template:PrimateTalk. -- User:Docu

I think that's a good idea. Let's then draft that message. PrimeFan 22:35, 23 Mar 2004 (UTC)

I like it. We could use "resource about numbers", instead of "number theory resource" as it's not stricly mathematical. "go to [Talk:WikiProject Numbers]" could also point here.-- User:Docu

I didn't mean to give number lore short shrift. But in a way, I'm starting to think of number lore as being part of number theory: why are certain numbers chosen by people to represent certain things? Anyway, I amended the draft per your suggestion, and I'd like to get some of the other project members to comment on it. PrimeFan 21:20, 24 Mar 2004 (UTC)

Draft MediaWiki NumberTalk Message

This article is part of Wikipedia:WikiProject Numbers, an attempt at creating a standardized, informative and easy-to-use resource about numbers and number theory. Suggestions for improving multiple articles on numbers and related subjects should go to Wikipedia talk:WikiProject Numbers.

I just created it: Template:NumberTalk. -- User:Docu

It looks very good, but there's just a tiny problem about the verbiage "number theory resource resource about numbers." I drafted an emendation above. PrimeFan 22:17, 2 Apr 2004 (UTC)

Looks like I copied and pasted a bit too quickly. I removed the <s> part. Please amended the message further if you like. -- User:Docu

Layout still not right

I wanted to see what we had on the tv series 24 so went to [[24]], not expecting a page on the tv series, but at least a link to it, or failing that, a link to a disambiguation page. But no, all I get is a link to [[Number 24]], which, buried in a list of properties of the number 24, has a link to the TV show named 24. This is unreasonably difficult -- I only found what I wanted because I know how WP works very well - a newbie or casual user will not be so lucky. What can we do in cases like this to make things easier for users? Pete/Pcb21 (talk) 09:14, 5 Apr 2004 (UTC)

For this specific case, I changed the disambiguation at year 24 AD so that it now has links to 24 (number) and 24 (television). We will have to identify similar situations before we can handle this in a uniform manner. PrimeFan 20:20, 5 Apr 2004 (UTC)

The current std format is defined on Wikipedia:WikiProject_Years#Template. For letters, I find the new format recently implemented allows to locate quite easily different uses of A, B, C, even if they are not listed on top of the page. Afterall, listing all uses on top of the page, isn't a std format. -- User:Docu

RFC: Roman numerals for large integers

User:Sverdrup thinks that for large integers like 2^31 - 1 we should state too large in the Roman numeral field of the Docuan table. I think we should just omit the Roman numeral field altogether in those cases. PrimeFan 20:36, 5 Apr 2004 (UTC)

I agree, let's remain flexible in which rows we use. -- User:Docu

Any number fans out there who speak Nahuatl?

I noticed that User:Glenn has been adding interwiki links to articles on numbers in the Nahuatl language Wikipedia; the one on 12 is located at Mahtlahtlinome. If anyone here knows someone who likes number theory and speaks Nahuatl, please let them know about the Nahuatl Wikipedia. PrimeFan 21:35, 8 Apr 2004 (UTC)

Table style

I urge everyone to put style = "margin-left: 0.5em;" in the table header. This will prevent the paragraph text to run all the way into the table border which otherwise will happen on certain browsers if the user has opted for justified paragraphs. Abigail 00:02, May 16, 2004 (UTC)

I see you have put that style specification in the Docuan tables for 145 and 147. I'm using Internet Explorer and I have never edited my Wikipedia Preferences, and I notice no difference in the number articles with and without that specification. But if this is a problem for a lot of users, then we should cooperate on gradually adding that style specification to all number articles. PrimeFan 18:56, 16 May 2004 (UTC)

If all tables need this change, it's probably a bug that should be submitted to Sourceforge or on Test, rather than fixed on every table.

Once we will be getting the new template namespace feature (started on Meta:), see Test:Template_testing, the formatting is defined in the template and just the params are defined in the article, e.g. Test:Mercury 3. Then it will be easier to fix this. -- User:Docu

I've just applied Abigail's fix to 42 (number) and it looks a lot better. It took me a long time to find somewhere that described this fix. Noisy 14:15, 2 Jul 2004 (UTC)

Order for mathematical properties?

XJam and I at the Slovene Wikipedia are wondering if there is an order for the mathematical properties of a number. For instance, I notice that PrimeFan tends to put heteromecic number ahead of Harshad number. Anton Mravcek 22:21, 18 May 2004 (UTC)

Here at the English Wikipedia we are still working on that. Generally, we want to keep related properties of a number together (such as perfect number and harmonic divisor), and we want to list base-independent properties first and base-dependent properties last. Of course, these two guidelines need to be prioritized sometimes. For example, if a number is a Mersenne prime and a palindromic prime, we might want to mention those two things together, before mentioning that the number is a centered hexagonal number. And some numbers might be so famous for one trait that it bears mentioning first, before anything else. PrimeFan 22:43, 18 May 2004 (UTC)

I don't think their gonna be many numbers past the first ten with so many mathematical properties that we need to worry about order. I say just try to determine which one is most important and work your way down to the least important (usually, the base-dependent ones). Numerao 18:27, 19 May 2004 (UTC)

Interwiki links

Do we have any standard proecdure for interwiki linking? Sometimes when I made a new number article in the spanish wikipedia I'd likn it here to the english wikipedia but I didn't always do that, and even if I did it consistently I only did it for english and not for the other ones. Numerao 18:30, 19 May 2004 (UTC)

I think the easiest way would be for each Wikipedian signed up to this project who is also working (or has worked) on number articles in another language Wikipedia to go through all the number articles in this English Wikipedia and make sure they all have links to the corresponding article in the other language Wikipedia (unless the other language Wikipedia doesn't have an article on that particular number). Then, after it is reported that that task is complete, the English Wikipedia will have the most complete interwiki linkage, and the Wikipedians from the other language Wikipedias can then look at the number articles in their respective Wikipedias and compare their interwiki linkages with those of the English Wikipedia.

So, Numerao, can I put you down as a volunteer to make sure all the number articles in the Spanish Wikipedia are linked to their counterparts in English? PrimeFan 20:25, 21 May 2004 (UTC)

You may want to try to get the Meta:Interwiki_bot to run (see also: Wikipedia:Bots). -- User:Docu

Shouldn't the number "1" have a link to "Benford's law" ? I'm far too thick to do it myself, but good luck to anyone who updates. User Phil in England ("O" level maths, grade "C")

== Large BFZO SJ KIFO éí DRTSD CST

n-gonal numbers

I propose the following:

Links like [[Polygonal number|Tridecaheptagonal number]] are to deprecated. They lead people to expect an article just on tridecaheptagonal number, for example, when they only lead to an article on polygonal numbers in general. Instead, the link should be made like this: k-gonal number.

Anton Mravcek 20:52, 22 Aug 2004 (UTC)

I agree with your proposal, misleading links to Polygonal number should be deprecated. I also agree with the replacing format. I'm going to see if I can change all the misleading links today. PrimeFan 20:34, 24 Aug 2004 (UTC)

Negative numbers

Would it be more convenient to simply redirect negative numbers to their absolute value? --Eequor 06:08, 24 Aug 2004 (UTC)

I'm not sure what the usefulness of such redirects would be. But perhaps I'm not so qualified to comment on this since my interests are focused more on positive integers. PrimeFan 21:41, 24 Aug 2004 (UTC)

At the moment only -1 and -40 would be redirected. Mainly, using redirects would allow all the properties for a given number (regardless of sign) to be on the same page. --Eequor 23:04, 24 Aug 2004 (UTC)

Negative one is an important, axiomatic number, clearly distinct from positive one, and definitely deserving of its own article. So I reverted your redirection. -40 is also distinct from +40, but I don't feel strongly enough about it to revert your redirect. PrimeFan 15:53, 25 Aug 2004 (UTC)

(Aha, I've found this discussion!) I had said a thing or two on Talk:-40 (number) but apparently these went unnoticed; and just as I was about to boldly go and redirect it, Eequor got to it first. I certainly agree that -1 deserves its own article, but the case for -40 is marginal, and I favor redirecting it. 4pq1injbok 19:16, 4 Sep 2004 (UTC)

Infobox

120

{{numbers (120s)}}
Cardinal	120 one hundred [and] twenty
Ordinal	120th one hundred [and] twentieth
Factorization	$2^{3}\cdot 3\cdot 5$
Divisors	2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60
Roman numeral	CXX
Prefixes	hecatontakaiicosa- (Greek)
Binary	1111000
Octal	170
Duodecimal	A0
Hexadecimal	78

At right is the infobox currently found in 120. Does this look about right? --Eequor 03:47, 26 Aug 2004 (UTC)

12

{{numbers (10s)}}
Cardinal	12 twelve
Ordinal	12th twelfth
Factorization	$2^{2}\cdot 3$
Divisors	2, 3, 4, 6
Roman numeral	XII
Binary	1100
Octal	14
Duodecimal	10
Hexadecimal	C

A similar set of templates can be found in 12. --Eequor 04:08, 26 Aug 2004 (UTC)

I dont know. The top line of numbers makes the whole thing looked too cluttered, imho. Plus the inclusion of greek prefixes for numbers beyong about 10 has no justification other than a desire for total thorouohgness. Niether profesional nor ametuer has use for things like that. Numerao 20:08, 27 Aug 2004 (UTC)

I agree that the very large Greek prefixes have little practical use, but they do have a consistent naming system which is rarely described in any detail. The prefixes are at least no less messy than writing out the name in English. --Eequor 20:35, 27 Aug 2004 (UTC)

As for more potential clutter, some of the Wikipediae in other languages have values of a few number-theoretic functions in these boxes. Do we want this sort of thing? 4pq1injbok 20:30, 4 Sep 2004 (UTC)

I like those number-theoretic functions in the infoboxes in the foreign Wikipedias. Even if I can't understand a word of the article, I can understand the infobox. As for having those in this Wikipedia, I don't know. I think we've got the interesting values of those functions covered in the articles (i.e., zeroes, highes and lowes of the Mertens function, nontotients, etc.). I for one would not oppose someone adding those number-theoretic functions to the infoboxes, but I hope anyone thinking about it discusses it here first. PrimeFan 22:10, 5 Sep 2004 (UTC)

These navigation links are based on the most recent discussion regarding such (found in /Archive 0), incorporating the style used by Sj. The previously used internal borders seem distracting to me. From earlier:

More choices for navigation bars (now also with tables): Template:Numbers_50s and Template:Numbers_60s:

List of numbers — Integer

50 -51 -52 -53 -54 -55 -56 -57 -58 -59 -60

59 -60 -61 -62 -63 -64 -65 -66 -67 -68 -69 -70 -71

List of numbers — Integer

0 -10 -20 -30 -40 -50 -60 -70 -80 -90 -100

They can be seen on white (article namespace) background on 55 (number) and 60 (number). If we use a table, we should probably avoid the <hr> mainly used for disambiguation. As on the default skin, the color #cccccc of table tends to rival with the one of the Wikipedia logo, I used a slightly grayed white on the msg versions above. Personally, I prefer the msg solution over sequence table inserted in the articles. -- User:Docu

I too prefer the msg solution. Reduces the possibility of human error and makes it easier to fix when it does happen. PrimeFan 16:47, 1 Mar 2004 (UTC)

As the msg are being edited, I placed the version available when posting a/m comment. In the meantime, I made the numbers a bit smaller, e.g. Template:Numbers_110s:

109 -110 -111 -112 -113 -114 -115 -116 -117 -118 -119 -120 -121

List of numbers — Integer

100 -110 -120 -130 -140 -150 -160 -170 -180 -190 -200

Personally, I think it's usefull if the 10/20/30 are also linked (either an all from 10-99 or just on 10/20/30/40. At some point we will have to chose which version we'd like to include in the template. -- User:Docu

This last version seems very good to me. All the links we need are included, and the layout is nice. slord 22:30, 11 Mar 2004 (UTC)

Prefix rows for the tables

Any corrections to the rows to the tables on the right of some of the number articles that mention 2 prefixes, one from Greek and one from Latin, for the numbers?? 66.245.112.43 21:48, 1 Sep 2004 (UTC)

I think it was User:Eequor who added all those. They look right to me, but it would be nice if a couple of different people scrutinized those. PrimeFan 20:42, 2 Sep 2004 (UTC)

Multiplication dots vs. crosses

Ldrhcp noticed a problem for the MediaWiki software when dealing with MathML cdots in the factorization fields of the Docuan tables. He changed the multiplication dots to crosses in the Docuan table for the article on 42 (number). Should this change be applied to all the articles on composite numbers, and is there a volunteer or robot to carry out the change? Anton Mravcek 15:51, 13 Oct 2004 (UTC)

I haven't noticed any problems. The cdots render just fine. Could you explain what is the nature of the problem MediaWiki is having? PrimeFan 21:05, 14 Oct 2004 (UTC)

Using \cdot renders as PNG, instead of either HTML or MathML. Images for equations don't scale up with fonts, sometimes have the wrong background color, and print poorly. Here is an example:

$5\times 4=20$ (<math>5 \times 4 = 20</math>

versus $5\cdot 4=20$ (<math>5 \cdot 4 = 20</math>. This is really more of a MediaWiki problem than a problem on the pages. --Ldrhcp 20:15, 15 Jan 2005 (UTC)

Categorization question

Should every integer be categorized directly into Category:Integers? For example, 2 (number) is categorized into Category:Prime numbers and many others which are subcats of C:Integers. Should all of these numbers be "double-categorized" as integers, or are the specific subcats enough? --Whosyourjudas (talk) 21:22, 27 Oct 2004 (UTC)

That's a very good question. Before answering it, though, I'm going to look at some other WikiProjects, see how they handle it. For example, for WikiProject Chemical Elements, would they categorize lanthanides directly into Chemical Elements, or into subcategory Lanthanides? I suggest other members of this project also look at other "double-categorization" possibilities that they can think of and report back here what they've seen and what they think would work best for this project. PrimeFan 21:30, 27 Oct 2004 (UTC)

Good suggestion. I checked WikiProject Countries - C:Poland is a subcat of C:Countries, and Poland is in both cats. --Whosyourjudas (talk) 21:53, 27 Oct 2004 (UTC)

I think we should also ask a MediaWiki programmer for input in this issue. Does category nesting and duplication (like in your Poland example) cause any real or potential difficulties for the MediaWiki software? Robert Happelberg 19:53, 28 Oct 2004 (UTC)

imho, we don't need so many categories. c:Integers is probly enough for this project. If like i'm reading the article on the number 1729, the main text already says its a Zeisel number, a Giuga number, and a Harshad number. If i want to know what other numbers are also Zeisel numbers, i can click the Zeisel number link, and it will tell me not just what other numbers are also zeisel numbers, it will also tell me just what the heck a Zeisel number. Let me see a category do that. Numerao 13:58, 29 Oct 2004 (UTC)

Commas for 10^3+

User:Sonjaaa thinks we should include commas in the title of the article on the number 10000. The change needs to be discussed and agreed upon because at least a dozen other pages would have to be changed to conform, namely, any page on a number greater than 999. PrimeFan 20:53, 10 Nov 2004 (UTC)

No. Do not include commas. This is not an international standard - some (I'm not sure if many) places use spaces for digit grouping - e.g. "10 000" to represent your "10,000" or "10000". I've also seen the comma used as the decimal separator, which would cause even more confusion. Keep the status quo. --Whosyourjudas (talk) 23:09, 10 Nov 2004 (UTC)

It's the English-language standard for an English-language Wikipedia. Other languages have other customs for decimals and digit grouping, but we are editing in English here, and I think clarity is greatly improved. Of course, years dont take the comma. --Sonjaaa 00:29, Nov 11, 2004 (UTC)

It's the American English standard for an international encyclopedia. According to comma and SI#SI writing style and the IEEE, the internationally accepted style regardless of language is spaces to separate groups of one thousand. So keep it like it is or go spaces, but not commas; international (even some British) English users could be confused. --Whosyourjudas (talk) 03:59, 11 Nov 2004 (UTC)

At Wikipedia:Manual of Style (dates and numbers), it says:

"Very large numbers, such as pinball scores, should be divided up by commas every three places. (Note that this is different from SI notation where a thin space is used every three places.) In scientific contexts, scientific notation is preferred."

This seems to be saying to me that for this case we should be looking at how professional mathematicians would more likely notate these numbers. Robert Happelberg 23:40, 14 Nov 2004 (UTC)

Special:Contributions/32.205.95.61

A anon user has been making some odd changes(for example, Number 2 changes) to a lot of number aticles recently; would someone look this over and decide what should left and what reverted? Also, it would probably be good to try to contact eim if possible. JesseW 11:03, 23 Nov 2004 (UTC)

I've been looking at the changes he/she made to the article on the number 3. Most of the letter combinations, (i.e., 3a, 3b,3c, etc.) are red, and the few that are blue are invariably redirects. It makes me wonder if this is the work of a deletionist trying to make a point. So I hesitate to revert anything in this case. Anton Mravcek 19:06, 23 Nov 2004 (UTC)

It's just 0 to 9, and it's because 0-9 are frequently the start of two character things, which don't seem to have too many occurances on WikiPedia at the moment, but it could in the future. It also matches it up against the latin alphabet (or English alphabet), as 0-9 are not just numbers. 132.205.95.65 19:16, 23 Nov 2004 (UTC)

What are some examples of "two character things"? And how does it (the changes, or something else?) match up with the latin alphabet? I don't understand. Would you explain further? JesseW 01:16, 24 Nov 2004 (UTC)

The latin alphabet letters has two letter combinations, and sometimes, letter-digit combinations at the end of each page. Even though many of the two letter combinations are redlinked, they've still been there for quite a while. The #D or #d combination meaning the n-th dimension is frequently encountered. 3M is a famous company from Minnesota. 3G is a common shorthand to refer to the next-gen cellphone tech. #x is commonly found to mean various things as a multiple of, like AGP 8x, also found just as 8x. 2L is a famous sound company. Several of these are also part of biochemical terminology for proteins and such. Ofcourse not everything has a wikipedia entry yet. They just illustrate that 0-9 are not just numbers, but symbols/characters of the English language commonly used in the wide world. 132.205.64.202 07:26, 24 Nov 2004 (UTC)

Ok, that makes sense to me now. Like F#See_also, right? Great, carry on. ;-) JesseW 14:35, 24 Nov 2004 (UTC)

Astronomical numbers

I believe it would be appropriate to include astronomical numbers in the Numbers space. I note that atomic numbers are included, and so too should be those pertaining to astronomical data, in particular Messier numbers, NGC numbers, and Saros numbers. I would appreciate hearing feedback. Denni☯ 23:16, 2004 Dec 2 (UTC)

I've come to agree with you. I have added the Messier numbers, NGC numbers, and Saros numbers to the outline on the project page. These three kinds of numbers appear standard enough to me. Now, the other project members and I need to draft some guidelines for the Criterion for including cultural associations section. We need to draw the line between information that is eternal (or at least eternal enough) like the fact that the solar system has 9 planets, and extremely ephemeral information, like a cloud in Wisconsin covering the moon for 9 minutes on such and such date. Anton Mravcek 00:18, 11 Dec 2004 (UTC)

I must admit I don't know much about astronomy or astrology. I have no idea where the line needs to be drawn for astral information. PrimeFan 21:22, 13 Dec 2004 (UTC)

Sorry to bring this up again, but I find these numbers quite arbitrary. -- correct me if I speak nonsense, since I am not an astronomer, nor a mathematician. It seems that it is just a numbered series like e.g. the richter scale, series of books/films/episodes and the like. Nothing special about the fundamental properties of the numbers in connection to the series except ordinality - the property of numbers that makes it useful in enumerating elements of a sequence. The primes, magic numbers all have something to do with that. The atomic numbers are achieved with strongly interwoven physical and mathematical properties. Cultural significance is another story, we might get into, but not yet. I propose removing this information after merging it with the appropriate page.

• Messier objects: why not list these objects in that article. And please add some info there on how this enumeration was achieved if it is something other than some arbitrary assignment (e.g. the order of discovery would be arbitrary, the spacial distance from some arbitrary other point in space is not)
• Saros numbers, I don't fully understand the article, it could do with a thorough rewrite, but it seems to be a chronological enumeration of solar cycles. Move information on significant cycles there.
• NGC numbers, create this article, list all relevant NGC's there, and remove from number-pages if assignment is again a simple enumeration.

To me it seems important to consider the way the astronomical numbers are "calculated". It should be clear from the articles, but it is not. (and why are there 2 saros series here (diff)? if that has something to do with the number 2, please explain how on that page.)

I don't know enough about the subject to rewrite it myself, but I hope someone does. I would be glad to assist. -- Zanaq 11:25, 1 October 2005 (UTC)

100%

The article 100% is about a game show. Shouldn't there be some sort of disambiguation notice on this, about the value's numerical significance (i.e. it is equal to 1). Maybe dab to 1 (number)? I'm not asure if there's a page that covers the idea of percentage values. --Whosyourjudas (talk) 21:53, 3 Dec 2004 (UTC)

RFC: Numbers in Statistics

In response to the creation of the article 6000000 (number), I have drafted guidelines for numbers in statistics in the project page. Project members, please read them and amend them if necessary. PrimeFan 22:18, 22 Dec 2004 (UTC)

432 (number)

I found the article 432 (number) via the addictive "Random page" button. I could be wrong, but it seems that many of the facts listed there don't actually pertain to the number 432. There are references to 43200, and LOTS of stuff about 108. Maybe one of the people involved in this project could take a look at it. Joyous 18:41, Dec 31, 2004 (UTC)

Thanks for noticing that. The article was created on December 30 in an orgy of mostly-anonymous edits. I've taken out all the false info, the stuff about 108, and the dubious stuff about human heartbeats and breaths. There's basically nothing left! If the project didn't specifically state that every number up to 1024 should have a page, I might nominate it for deletion. Dbenbenn 02:03, 2 Jan 2005 (UTC)

Alright, the same user added the same "information" again, and I'm about to remove it again. I'd appreciate anyone else's comments or contributions at Talk:432 (number). Dbenbenn 23:47, 6 Jan 2005 (UTC)

I wrote "continuous -1 to 1024" as a proposal. Now I think "continuous -1 to 256" might be a more reasonable goal. Even if this new specification is accepted by all the project members, I hesitate to refer 432 to VfD because I have the suspicion that the anonymous user is a deletionist trying to make the point that there shouldn't be articles on any number whatsoever. PrimeFan 21:33, 7 Jan 2005 (UTC)

"See also" section for digits

An anon (Special:Contributions/132.205.95.61) added a "see also" section to 1 through 9 that look like this:

Digit-letter combinations starting with 8:

• 8a 8b 8c 8d 8e 8f 8g 8h 8i 8j 8k 8l 8m 8n 8o 8p 8q 8r 8s 8t 8u 8v 8w 8x 8y 8z
• 8A 8B 8C 8D 8E 8F 8G 8H 8I 8J 8K 8L 8M 8N 8O 8P 8Q 8R 8S 8T 8U 8V 8W 8X 8Y 8Z

I don't see the point, so I've removed them. The only non-red links were

0d, 0s, 0x, 0G, 1d, 1G, 1P, 2d, 2D, 2G, 2P, 2R, 3d, 3g, 3i, 3B, 3C, 3D, 3G, 3M, 3T, 4d, 4h, 4D, 4G, 4H, 4S, 4X, 5K, 5M, 7z, 8X, and 9P.

Dbenbenn 02:41, 2 Jan 2005 (UTC)