Talk:Sexy prime

Sexy prime sextuple

Why are they not defined as the numbers n such that exactly five of n, n+6, n+12, n+18, n+24 and n+30 are all prime, and the other is 5 times a prime? E.g., if n=990359, then n, n+12, n+18, n+24 and n+30 and (n+6)/5 are all prime.

Sexy prime quintuple

Why are the sexy prime quintuples not defined by the numbers n such that exactly four of n, n+6, n+12, n+18 and n+24 are prime, and the other one is 5 times a prime? E.g. why is n=7817 not start of any prime quintuple although n, n+6, n+12, n+24 and (n+18)/5 are all prime?

Untitled

I changed "such that p + 18 is composite " to "prime" . Please someone change back if it is wrong, but the examples are prime and it makes more sense as prime.

Walt 20:37, 4 April 2006 (UTC)

Ooops! - put it back, I had missed that it was the first one _not_ in the triplet that is not prime.

Walt

Sexy twin primes?

Is there a name for sexy pairs of twin primes, i.e. sets of four primes of the form (x, x+2, x+6, x+8)? The first four such sets are (5, 7, 11, 13), (11, 13, 17, 19), (101, 103, 107, 109), (191, 193, 197, 199). It is easily proven that for all "sexy twin primes" except (5, 7, 11, 13), x mod 210 must be 11, 101, or 191. --12.34.246.38 21:18, 4 August 2006 (UTC)

It's called a Prime quadruplet. --PrimeHunter 22:52, 4 August 2006 (UTC)

Ah! Okay, thanks! --12.34.246.38 18:14, 8 August 2006 (UTC)

Um, Actually, no it's not. That would be (x, x+2, x+4, x+6). This is quite different. There's no word for this, really, as it's pretty much an arbitrary pattern. A lot of cool patterns just don't have names, just because there's so many of them that it doesn't make sense to try naming them all. -- Aljo September 13, 2006

Did you look at the Prime quadruplet article? It is easily proven that there are no sets of primes of the form {x, x+2, x+4, x+6} (with the dubious exception of {1, 3, 5, 7} if you consider 1 a prime, which most mathemeticians do not). In fact, in any group of three numbers of the form {x, x+2, x+4}, one will always be a multiple of 3, so the only way they could all be prime is if 3 itself is one of them, as is the case for {3, 5, 7}. --Mwalimu59 16:27, 13 September 2006 (UTC)

Consecutive primes

I am studing the sucession 3-2,5-3,7-5,11-7 and so on and I have found that 6 is the predominant number and my question is, why??? from España/Manuel l. — Preceding unsigned comment added by 217.125.114.57 (talk)

I am not sure what you mean by predominant number. All primes above 3 are of form 6n-1 or 6n+1 (otherwise they would be divisible by 2 or 3). And 6 is the "jumping champion" (most common prime gap [1]) for some small numbers and from 947 to perhaps around 10³⁵. PrimeHunter 00:35, 23 March 2007 (UTC)

Thank you ,this is what i was looking for (for me,predominant=champion).Manuel López(España)

What is # ?

p = (48011837012 · ((53238 · 7879#)2 - 1) + 2310) · 53238 · 7879#/385 + 1 What is the "#"??

The end of the following line said "7879# is a primorial". I have moved it to the start of the line. PrimeHunter 11:29, 2 January 2007 (UTC)

Missing prime triplets

The list of sexy prime triplets misses loads of triplets out e.g. (5,11,17) (11,17,23) (41,47,53) someone change it!!! --Steph and Jacob 86.128.7.144 (talk) 22:23, 12 June 2008 (UTC)

The definition says p + 18 must be composite. This is in agreement with the MathWorld and OEIS sources. The list is correct for that definition. I personally don't like that definition but Wikipedia articles should be based on reliable sources. Do you know a reliable source which allows prime p + 18 in a sexy prime triplet? PrimeHunter (talk) 00:56, 13 June 2008 (UTC)

I agree that the "p + 18 must be composite" provision doesn't make much sense. It would make more sense if there was a similar provision that "p - 6 must be composite", which would disqualify any triplets that were part of a quadruplet; as it stands now it disqualifies the first three of a quadruplet but still allows the second through fourth of a quadruplet. Having neither provision (as the original comment implies) would work too, but having one and not the other doesn't make much sense to me. Furthermore I would note that there is no similar restriction on sexy prime pairs, so why should there be on triplets? --Mwalimu59 (talk) 17:54, 13 June 2008 (UTC)

neologism?

I'd like to see some evidence that this term is actually used in the literature, and isn't just another of Eric Weisstein's annoying neologisms.

Google Scholar finds very few hits, and most of them appear unrelated (things like "sexy prime-time hostess"). There are two sort-of-legitimate hits, but they're kind of borderline: One quotes Weisstein for the name and is largely about teaching. The other is an undergrad honors thesis. --Trovatore (talk) 23:24, 3 May 2009 (UTC)

I am quite sure that it is. I remember reading this term quite often in textbooks. However, it is best to wait for other opinions. --PST 03:30, 4 May 2009 (UTC)

Search on "sexy primes" [2] instead of "sexy prime". PrimeHunter (talk) 08:55, 4 May 2009 (UTC)

Ah, OK, that seems to be a reasonable amount of attestation. However it does raise the question whether the article ought to be at sexy primes, as an exception to the usual convention, given that there doesn't seem to be much guidance in the literature as to what a single sexy prime is, if anything. (That was the question that actually drew my attention here — reading the current lede literally, it appears that a sexy prime is not a prime number at all, but rather a pair of prime numbers.) --Trovatore (talk) 09:30, 4 May 2009 (UTC)

I wouldn't mind seeing an etymology section! - Letsbefiends (talk) 08:27, 20 June 2012 (UTC)

The article says it's just a play on the Latin word for 'six'. There's nothing more to explain in an etymology. Mal7798 (talk) 01:47, 24 September 2013 (UTC)

p+18 is composite?

It appears there have been several attempts to add sexy prime triplets that did not meet the qualification that p+18 is composite, all of which have been reverted. I'm not questioning that the reverts are correct if one accepts the "p+18 is composite" qualification. I would like to ask, however, where that qualification comes from. After reviewing the named patterns in the Prime k-tuple article, it appears that sexy prime triplet is the only one that has an additional qualification that some number less than or greater than or within the pattern must be composite, and the list of sexy primes (p, p+6) has numerous examples where p+12 is also prime. It seems inconsistent that this one prime pattern has this added requirement when none of the others do. Are there any reliable sources to support the "p+18 is composite" qualification? If so, should any of the other prime patterns have a similar qualification? mwalimu59 (talk) 19:37, 14 December 2014 (UTC)

Is there any reliable source which does not say it? It's a rare term and the p+18 condition is in all three OEIS sequences in the sexy prime triplet section (OEIS: A046118, OEIS: A046119, OEIS: A046120), and the references section says:

• Weisstein, Eric W. "Sexy Primes". MathWorld. Retrieved on 2007-02-28 (requires composite p+18 in a sexy prime triplet, but no other similar restrictions)

PrimeHunter (talk) 23:32, 14 December 2014 (UTC)

is this notable?

Why is this a thing? Is it a useful concept? Does it take one farther into understanding numbers? --Richardson mcphillips (talk) 01:44, 20 April 2015 (UTC)

In Wikipedia, "notable" means satisfying Wikipedia:Notability or one of the subject-specific guidelines like Wikipedia:Notability (numbers). That appears to be the case for sexy primes. In an earlier section I posted the Google Scholar search [3]. If they had not been named but were just described in sources with something like "primes separated by six" then we probably wouldn't have an article. Sexy primes are mathematically similar to twin primes but there is far more interest in the latter. Sexy primes do not appear useful but the same can be said about a large part of mathematics. PrimeHunter (talk) 02:54, 20 April 2015 (UTC)

Thanks. Richardson mcphillips (talk) 20:29, 30 May 2015 (UTC)

EXACTLY! IS THIS A THING? ARE THERE QUINTY PRIMES TOO? — Preceding unsigned comment added by Wlexxx (talk • contribs)

For Wikipedia it's a thing if published reliable sources talk about it. A Google search finds results on "sexy primes" but not "quinty primes" so the latter doesn't appear to be a thing. I'm not sure what you imagine quinty primes would be. "quint" is usually something with 5 but all primes above 2 are odd so the only primes which differ by 5 are 2 and 7. That would be strange to name. The only named differences I know are twin primes (2), cousin primes (4), and sexy primes (6). I'm a prime geek and have found probable primes (prp's) above 10000 digits with all even differences from 8 to 100: http://www.mersenneforum.org/showthread.php?t=11381#10. Somebody actually mentioned my cousin prp record from that post in Cousin prime#Properties but only credited the discoverers of the prime p = 474435381 · 2⁹⁸³⁹⁴ − 1. They may not know I seven years later found that p − 4 is prp. PrimeHunter (talk) 15:54, 28 February 2017 (UTC)

Only on Wikipedia

Could you find an article half as funny as this one. MightyArms (talk) 03:35, 5 February 2022 (UTC)

what about Wikipedia:List_of_really,_really,_really_stupid_article_ideas_that_you_really,_really,_really_should_not_create Awesomecat713 (talk) 00:50, 19 May 2022 (UTC)

What does n# mean?

I see the notation n# used on this page a lot—for example, 2521#. What does this mean? DaBOXEN (talk) 23:22, 13 November 2023 (UTC)

@DaBOXEN: See the first section: Sexy prime#Primorial n# notation. PrimeHunter (talk) 00:03, 14 November 2023 (UTC)