Talk:Sexy prime

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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

Contents 1 Sexy twin primes? 2 Consecutive primes 3 What is # ? 4 Missing prime triplets

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)