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?

Restriction that n+18 is composite for prime triples is crazy!
Without restriction that n+18 must be composite, this sequence would be:

Numbers n such that n, n+6 and n+12 are all prime.

5, 7, 11, 17, 31, 41, 47, 61, 67, 97, 101, 151, 167, 227, 251, 257, 271, 347, 367, 557, 587, 601, 607, 641, 647, 727, 941, 971, 1091, 1097, 1117, 1181, 1217, 1277, 1291, 1361, 1427, 1447, 1481, 1487, 1601, 1607, 1657, 1741, 1747, 1777, 1861, 1867, 1901, 1987, 2131, 2281, 2371, 2377, 2411, 2671, 2677, 2687, 2707, 2791, 2897, 2957, 3301, 3307, 3457, 3527, 3631, 3727, 3911, 3917

There are 2900 terms up to 1000000. They are:

1 5 2 7 3 11 4 17 5 31 6 41 7 47 8 61 9 67 10 97 11 101 12 151 13 167 14 227 15 251 16 257 17 271 18 347 19 367 20 557 21 587 22 601 23 607 24 641 25 647 26 727 27 941 28 971 29 1091 30 1097 31 1117 32 1181 33 1217 34 1277 35 1291 36 1361 37 1427 38 1447 39 1481 40 1487 41 1601 42 1607 43 1657 44 1741 45 1747 46 1777 47 1861 48 1867 49 1901 50 1987 51 2131 52 2281 53 2371 54 2377 55 2411 56 2671 57 2677 58 2687 59 2707 60 2791 61 2897 62 2957 63 3301 64 3307 65 3457 66 3527 67 3631 68 3727 69 3911 70 3917 71 4001 72 4007 73 4127 74 4451 75 4507 76 4591 77 4637 78 4651 79 4787 80 4931 81 4987 82 5101 83 5107 84 5297 85 5381 86 5387 87 5407 88 5431 89 5437 90 5471 91 5557 92 5641 93 5647 94 5737 95 5801 96 6067 97 6257 98 6311 99 6317 100 6361 101 6367 102 6857 103 6971 104 7207 105 7517 106 7577 107 7817 108 7867 109 8081 110 8111 111 8231 112 8707 113 8741 114 9001 115 9337 116 9391 117 9461 118 9467 119 10247 120 10331 121 10601 122 10651 123 10847 124 11491 125 11777 126 11801 127 11821 128 11827 129 11897 130 11927 131 12037 132 12101 133 12107 134 12491 135 12541 136 12577 137 12641 138 12647 139 12911 140 12967 141 13037 142 13171 143 13451 144 13457 145 13681 146 13751 147 13901 148 14537 149 14551 150 14621 151 14627 152 14741 153 14747 154 15187 155 15307 156 15461 157 15727 158 15761 159 15791 160 15797 161 15901 162 15907 163 16057 164 16061 165 16091 166 16217 167 16421 168 16481 169 16561 170 16931 171 16981 172 17021 173 17041 174 17321 175 17377 176 17471 177 17477 178 18121 179 18211 180 18217 181 18301 182 18427 183 19207 184 19417 185 19421 186 19457 187 19471 188 19477 189 19571 190 19597 191 20101 192 20117 193 20341 194 20347 195 20747 196 21011 197 21157 198 21481 199 21487 200 21517 201 21557 202 21991 203 22067 204 22147 205 22271 206 22441 207 23197 208 23321 209 23327 210 23741 211 23761 212 23887 213 24071 214 24091 215 24097 216 24407 217 24671 218 25457 219 25577 220 25667 221 26107 222 26171 223 26177 224 26387 225 26681 226 26687 227 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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 ) 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. -- PS T  03:30, 4 May 2009 (UTC)
 * Search on "sexy primes" 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 &mdash; 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, and the references section says:


 * 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 Notability or one of the subject-specific guidelines like Notability (numbers). That appears to be the case for sexy primes. In an earlier section I posted the Google Scholar search . 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 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 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)
 * See the first section: Sexy prime. PrimeHunter (talk) 00:03, 14 November 2023 (UTC)