Wikipedia:Articles for deletion/Bell's prime number theorem

The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was delete. Can't sleep, clown will eat me 10:40, 2 August 2007 (UTC)[reply]

Bell's prime number theorem[edit]

Named "theorem" with zero Google hits and zero sources. Violates WP:OR, WP:V, WP:N. Creator removed prod without giving a requested source [1], and concedes being unable to prove it's by Bell.[2] As explained at Talk:Bell's prime number theorem, the result is a trivial consequence (at least for a mathematician) of p²-1 = (p-1)×(p+1), so my OR concern is mainly about the name and claim it's by Bell. No known source mentions this result, and it seems questionable to call it a theorem (a word usually used about harder things). Author has mentioned possibility of rename. This might fix the OR and V problems, but it's still non-notable. It appears a trivial and uninteresting observation that is not worth merging anywhere. A mathematician could make scores of similar observations about divisibility properties of specific polynomials. PrimeHunter 00:33, 30 July 2007 (UTC)[reply]

Delete per nom -- total hoax and WP:OR. My math skills aren't that advanced, so I'm trusting the nom's skills. Ten Pound Hammer • ^{(Broken clamshells•Otter chirps•Review?)} 00:38, 30 July 2007 (UTC)[reply]
- Comment You know, out of my curiosity, I decided to verify what he says, although it is just pure common sense at times. A prime number p greater than 3 must be odd and have a least significant digit of either 1, 3, 7 or 9. It definitely is not divisible by 3. p-1, p and p+1 span a range of 3 numbers, so either p-1 or p+1 must be divisible by 3. At the same time, both p-1 and p+1 are even, and since their difference is 2, one of them must be divisible by 4 as well. So, multiplying both of them together would give something that is divisible by both 8 and 3, and hence p² - 1 is divisible by 24. There you go.--Kylohk 01:07, 30 July 2007 (UTC)[reply]
  - Comment. Excellent! Now please proof read Original proof of Gödel's completeness theorem (just kidding). PrimeHunter 01:30, 30 July 2007 (UTC)[reply]
Delete It's true that there are no search results for this theorem. It may or may not be true, but if no other academic sources mention it, it's likely to be OR, and not suitable for wikipedia. Better wait until at least 1 textbook mention his "theorem".--Kylohk 00:48, 30 July 2007 (UTC)[reply]
Delete Almost trivial factoid about prime numbers which was most likely known way before Bell even learned to read. It may still be that somebody, somewhere decided to name this factoid Bell's prime number theorem but from a mathematical standpoint, that somebody was misguided and I don't believe anyone has followed suit. Pascal.Tesson 02:46, 30 July 2007 (UTC)[reply]
Keep Everyone agrees that this theorem is true. PrimeHunter, an expert in prime numbers, believes that it is trivial for him (though his proof about p>=17 is scarcely convincing) but it is original researchto deduce that it is trivial for others, and despite the supposed triviality he did not know the result already. If it is not by Bell, the article could be renamed, but not deleted. As for original research, it cannot be both trivially, obviously true and a dubious piece of original research.--Bedivere 06:05, 30 July 2007 (UTC)[reply]
- Comment. Wikipedia is not for everything that is true. See Wikipedia:What Wikipedia is not and Wikipedia:Notability. This result sounds like something that might be asked as an easy exercise to students. A harder exercise might be: Prove "PrimeHunter's prime number observation": If p is a prime above 61, then (p⁶⁰-1)/6814407600 is a composite integer. That doesn't mean we should create PrimeHunter's prime number observation. PrimeHunter 14:15, 30 July 2007 (UTC)[reply]
- Query Bedivere, we really need the answer to this question: Have you seen some book or scholarly article that either called this something like "Bell's prime number theorem" or attributed it to Eric Temple Bell? If so, which book or journal? Tell us enough so that we can go to the library and find it. Michael Hardy 19:53, 30 July 2007 (UTC)[reply]
Weak keep if textbook uses appear. If this is the way its taught to students, it should have an article.DGG (talk) 06:11, 30 July 2007 (UTC)[reply]

The problem being that there isn't a single reference supporting this use. The prime number theorem is a deep result in number theory and no scholar would be foolish enough to name anything "X's prime number theorem" when it has nothing to do with the distribution of primes. I have 4 number theory textbooks right here in my office, none of which support this terminology. Pascal.Tesson 15:03, 30 July 2007 (UTC)[reply]

Delete. The connection with Bell is not verifiable, and the result itself is too trivial (or not notable, in Wikipedia-speak) to have an article. The article should be kept if the theorem is stated as an important result in books or articles, but I doubt that will be the case. -- Jitse Niesen (talk) 07:04, 30 July 2007 (UTC)[reply]
Keep. May be integrated at some point. Gregbard 15:14, 30 July 2007 (UTC)[reply]
Delete (at most, put to a page where trivial fact about prime numbers are stated). Jakob.scholbach 00:38, 31 July 2007 (UTC)[reply]
Delete. There are no sources to connect this theorem with Eric Bell, and I believe the claims made above that the result is not notable. EdJohnston 01:01, 31 July 2007 (UTC)[reply]
Delete per nom. Oli Filth 01:18, 31 July 2007 (UTC)[reply]
Move or Merge With a simple google search I found these: [3] [4] [5] and this slight twist of subtracting the square of two primes:[6] (which has been known since at least 1878: [7]), so the zero google hits in the nom is incorrect. Also deleting every math topic not interesting to a mathematician is ridiculous--WP is for everybody. Agree that attributing it to Bell is unsupportable, so a move with history and delete the redirect would be appropriate. Dhaluza 02:52, 31 July 2007 (UTC)[reply]
- This does not show notability; it's just an isolated fact. For instance, the last but one link, which has the generalization that the difference between the squares of two numbers is divisible by 24, mentions "This is an observation i made one night while trying to go to sleep". Not every verifiable fact belongs in Wikipedia. -- Jitse Niesen (talk) 03:26, 31 July 2007 (UTC)[reply]
- Comment. Good find. Zero Google hits referred to the alleged name. None of your links mention Bell and none of them call it a theorem. They don't mention that (p²-1)/24 is composite for large p. And prime numbers is mathematically a red herring: The divisibility by 24 holds for any integer p that is not divisible by 2 or 3. The observation about 24 dividing p²-1 for prime p > 3 has been mentioned by some sources but it appears unnamed (a sign that it's not important) and I don't see what it could be moved to. I don't think the mentioned sources are enough for own article per WP:N, and there is not enough material for a meaningful article. A merge would leave a redirect on an apparently non-existing name, and there is no edit history that matters since a source can be quoted directly for the single line that remains if the unsourced part is removed. If references giving more significant coverage in multiple reliable sources are not found, then I think the one-line observation could be added to an existing article, either Prime number#Properties of primes or Square number#Properties. Bedivere can add it if he/she wants the edit. PrimeHunter 03:58, 31 July 2007 (UTC)[reply]
  - It could be meged to 24 (number) and/or Prime number for example. I agree that a redirect from this name is problematic, but I don't know what else to do. We could move this to 24 mystery per the first web page. This is also a one-source name, but at least it does not involve a person. I disagree that the lack of a name makes it unimportant. There are also textbook problem references if you take the search to Google Books. Dhaluza 04:30, 31 July 2007 (UTC)[reply]
Delete – unless someone comes up with a reliable sources attributing this as a theorem to ETB. --Lambiam 05:38, 31 July 2007 (UTC)[reply]
Merge into Eric Temple Bell. I have read one of his non-fiction books (re: Mathematicians). So it seems to fit there in his bio. Ghits are not perfect. Possibly needs more expert attention. Bearian 19:52, 31 July 2007 (UTC)[reply]
- Comment. Are you saying you have seen this in a book by Bell? It's true that GHits are not perfect, and it's possible but currently unverified that Bell has ever mentioned this observation. Dhaluza found multiple mentions of the result and none of them mention Bell (one was from before his birth). PrimeHunter 20:22, 31 July 2007 (UTC)[reply]
  - Comment I see two possibilities. Either this was never claimed by Bell as a theorem of his in which case it has no business in his article or Bell did claim this as his. In which case he was somewhat of a clown since this cute factoid is trivial and has nothing to do with primes as noted above. Either way, this has no business in his article. Pascal.Tesson 20:57, 31 July 2007 (UTC)[reply]
Merge into Prime number and, as a second idea, into Eric Temple Bell The first one makes sense, the second one can be corrected by editing if someone acquainted with Bell's works knows that it's not his original idea. Mandsford 00:55, 1 August 2007 (UTC)[reply]

So far two commenters have wanted this to be merged into Eric Temple Bell. But one reason for this AfD is that there is no evidence connecting this theorem to Bell, so his article is not an appropriate merge target. EdJohnston 02:01, 1 August 2007 (UTC)[reply]

Delete - despite several requests, there is no source that actually connects this "theorem" to ETB. Without a verification of this supposed connection, all that remains is a trivial and non-notable factoid about numbers that are co-prime to 24. Gandalf61 18:33, 1 August 2007 (UTC)[reply]

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.