Talk:Sphenic number

Untitled

I object to Ams80 calling mathematical facts such as Catalan numbers and pentagonality "pointless trivia"; facts such as these are extremely relevant to articles about numbers. But I don't object to Ams80 removing those facts from this page, since those facts at least are stated in the pages on the individual numbers in question. PrimeFan 23:11, 14 Feb 2004 (UTC)

Maybe I should clarify, I didn't mean to say, and don't believe, that concepts such as Catalan numbers and pentagonality are "pointless trivia". What I meant to say was that, for example, the fact that 105 is 12-agonal, is completely irrelevant to the topic of the page, that is why I viewed the entries as pointless trivia. I think that lists should only include information on the list elements if it is in some way relevant, for example at Trinity College, Cambridge it makes sense to me to have information about why notable alumni are notable but I wouldn't expect information completely unrelated to being an alumni listed, such as how many children they had, or where they were born. Information like that should be in the article about the person, and I feel the same way about the numbers in this article, trivia unrelated to number x being a sphenic number should be in the article about number x (if anywhere). Just my opinions -- Ams80 00:10, 15 Feb 2004 (UTC)

Now I understand where you're coming from and I agree with you. Thanks for clarifying. PrimeFan 17:18, 16 Feb 2004 (UTC)

Is it quite right to say "Currently, the largest known sphenic number is [...] i.e., the product of the three largest known Mersenne primes"? Would it not be better to say simply "Currently, the largest known sphenic number is [...] i.e., the product of the three largest known primes" adding, if required "(which are Mersenne primes)". Richard Pinch 21:23, 24 August 2006 (UTC)[reply]

Sphenic?

Where does the name sphenic come from? [1] gives 1,710 hits most of which are Wikipedia clones. [2] cuts this down to 109, and many of those seem to be based on Wikipedia. (sequence A007304 in the OEIS) does not use the word. --Henrygb 16:52, 29 Apr 2005 (UTC)

To be quite frank, I would love to know the precise etymology myself. I am

perhaps most to blame for this article title being used here. The source *I* had for the term is the Funk & Wagnalls Standard Dictionary (International Edition 1964).

I find it hard to believe they were copying wikipedia back in 1964, as that would create a timelike-loop somewhere along the road; but still where *they* got the term is very curious, if not odd... -- User:Cimon avaro

I'm not sure anyone really knows the answer to this question, but the term comes from Gk sphen, meaning wedge. If one looks at the Greek delta (Δ) as a possible Greek conception of a wedge, it is not hard to conceive the origin of the connotation of the number 3. Lself 07:09, 4 December 2006 (UTC)[reply]

There is a small, but non nil, chance that that was a Fictitious entry in Funk & Wagnalls, just included to catch other reference works pilfering from theirs. --Cimon Avaro; on a pogostick. (talk) 06:22, 12 September 2011 (UTC)[reply]

Stub?

Is this really a stub? It seems pretty much everything that can be said has been said (unless sphenic numbers have applications I'm not aware of).

Meekohi 20:39, 1 January 2006 (UTC)[reply]

I concur, as per the last paragraph of this fine mini-essay. -- Cimon Avaro; on a pogostick. (talk) 00:19, 12 September 2011 (UTC)[reply]

Definition unclear

Should say "three of its own distinct factors". Also if these are the only factors, we should say so as the article then implies they are: It says there are 8 factors of a sphenic number and then lists them. The definition is ambiguous. Anyway, I've "fixed" it and I hope it is correct! Paul Beardsell 10:24, 9 October 2006 (UTC)[reply]

I am formulating the definition to simply say "the product of three distinct prime numbers". I think this is short and clear. If anyone is in doubt anyway, the next sentence says squares are not allowed. PrimeHunter (talk) 15:00, 19 October 2006 (UTC)[reply]

Every four consecutive integers

I changed the part " ...because one of every four consecutive integers is divisible by 4..." to "...because one of every four consecutive integers (except the numbers ranging from -3 up to 3) is divisible by 4..." simply because the statement was incorrect, though I don't like this solution, can someone please create a better looking solution, or point out that the statement was correct? Blodskaal 10:37, 8 Apr 2009 (West-European Time)

I changed it to " ...because one of every four consecutive positive integers is divisible by 4..." [3]. This seems a better solution to me. Sphenic numbers are defined as positive integers in the opening line. Limiting the argument to positive integers avoids an irrelevant discussion about negative numbers and the status of 0. PrimeHunter (talk) 00:01, 9 April 2009 (UTC)[reply]

Connection with the Ulam spiral?

The main article could be improved if there were a chart showing how sphenic numbers occur when plotted out on a rectangular grid, sort of like the way prime numbers are distributed in an Ulam spiral. 216.99.198.25 (talk) 08:43, 26 October 2009 (UTC)[reply]

I don't think any source has done that for Sphenic numbers or mentioned the possibility so I don't think we should do it either. It's not common to do it for other sets than prime numbers. If we do it then it may seem like it should have some special significance for sphenic numbers but that is close to original research. PrimeHunter (talk) 12:57, 26 October 2009 (UTC)[reply]

The point

If there's a point to these numbers, can someone make clear in the article what that point is? It feels as though if mathematicians bothered to highlight them and give them a name, it was because they were found useful for some purpose further on in mathematical theory. If so, that isn't clear from the article.

As it is (with one exception: the mention of cyclotomic polynomials), all the article does is define them and then present a number of properties of theirs that, to anyone who understands prime numbers, are self-evident. (If you multiple a sphenic number by any integer greater than 1, the product won't be a sphenic number? A sphenic number has exactly eight divisors? The greatest known sphenic numbers is the product of the three greatest known primes? They're squarefree? The value of the Mobius function on these numbers (defined as having three distinct prime factors) is the value Mobius function for all numbers that have an odd number of distinct prime factors? Duh.) And then trivia like what the lowest two adjacent sphenic numbers happen to be. All of which lead me as a reader to ask if there's anything to them beyond the obvious.

If there isn't any further point and they're just a party game, I guess that's fine, but it just seems like there would be more. Largoplazo (talk) 22:31, 30 November 2024 (UTC)[reply]