Identification of Two (2) Primes Forming a Sexy Prime

[Harry Neel]

Greetings All:

Does OEIS have recommended terms or phrases for referring to two (2) primes that have a difference of six (6) and not to refer to them as a 'sexy prime pair' or 'a pair of sexy primes?'

Best Regards,

HN

[Dave Consiglio]

Sixy primes?

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[Robert Israel]

You could just call them A023201 (n) and  A046117(n).

Cheers,

Robert

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[Jonas Karlsson]

Or in pidgin-ancient Greek, hexapostatic primes (my attempted rendering of six-off-standing, take with a grain of salt). 

J

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[Bob Lyons]

‘The term "sexy prime" is a pun stemming from the Latin word for six: sex.’

— https://en.wikipedia.org/wiki/Sexy_primes

Bob

On Dec 2, 2025, at 4:56 PM, Harry Neel <neel...@gmail.com> wrote:

Greetings All:

Does OEIS have recommended terms or phrases for referring to two (2) primes that have a difference of six (6) and not to refer to them as a 'sexy prime pair' or 'a pair of sexy primes?'

Best Regards,

HN

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[Arthur O'Dwyer]

FWIW, I interpreted the original question (almost certainly incorrectly) as asking whether there's a good way in English to distinguish a related pair from an unrelated pair:

- 5 and 11 are a pair of sexy primes. (True in the expected sense.)

- 5 and 17 are a pair of sexy primes. (Still true, in that both 5 and 17 are sexy primes, and there are two of them, which makes a pair.)

The same question could be asked of twin primes: Is (3, 41) a pair of twin primes? And if not, what is it a pair of, then?

–Arthur

On Tue, Dec 2, 2025 at 6:23 PM Bob Lyons <bobly...@gmail.com> wrote:

‘The term "sexy prime" is a pun stemming from the Latin word for six: sex.’

— https://en.wikipedia.org/wiki/Sexy_primes

On Dec 2, 2025, at 4:56 PM, Harry Neel <neel...@gmail.com> wrote:

[Allan Wechsler]

My understanding was that Harry wanted a synonym for "sexy prime" because he thought that term was too goofy or naughty or something. My guess is that unless he wants to make up his own word, like Jonas did, that he'll be out of luck. Yes, it's a goofy term, but it seems to have traction and be fairly widely used.

-- Allan

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[Neil Sloane]

"Sexy prime"  is a scholarly joke (based on Latin), and it has been in the database since 1965. 

 

Best regards

Neil 

Neil J. A. Sloane, Chairman, OEIS Foundation.

Also Visiting Scientist, Math. Dept., Rutgers University, 

Email: njas...@gmail.com

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[Harry Neel]

    In an effort to be concise an important part of my question was deleted. So to retrofit: "When submitting any sequence that mentions sexy prime pairs, a pair of sexy primes, etc., are there prefencers for describing two sexy prime numbers in the definition, comments, examples, and so on, of a submittal.  What is a satisfactory definition for sexy prime in situations where one may be tempted to specify a pair of primes?

The original query was too long and when I shortened it the relevant parts were chopped.

Apologies to all, but I think I now know why the 'poor guy,' and 'the 'ha ha's' responses. (Not quotes of actual comments.)

Too Long Again, I know.

Regards,

Harry

[Gareth McCaughan]

On 04/12/2025 18:37, Harry Neel wrote:

    In an effort to be concise an important part of my question was deleted. So to retrofit: "When submitting any sequence that mentions sexy prime pairs, a pair of sexy primes, etc., are there prefencers for describing two sexy prime numbers in the definition, comments, examples, and so on, of a submittal.  What is a satisfactory definition for sexy prime in situations where one may be tempted to specify a pair of primes?

The original query was too long and when I shortened it the relevant parts were chopped.

Perhaps it's just me, but I find myself just as confused as I was after reading Harry's initial question. Possibly more confused.

The initial question said "... and not to refer to them as a 'sexy prime pair' or 'a pair of sexy primes'". The thing that remains completely unclear to me is: The usual way to refer to such a pair of primes _is_ to call them "sexy", so is Harry (1) asking whether OEIS has some preference for avoiding that word, or (2) saying that _he_ has a preference for avoiding that word and asking for good alternatives, or (3) talking about a situation where somehow that word is _incorrect_, or (4) something else?

If (1), it sounds from all the responses as if OEIS has no such preference. If (2), the obvious thing to say would be something like "pair of primes differing by 6". If (3), it would be good to have some clarification about what sort of situation Harry has in mind that would make the usual term incorrect (e.g., Arthur's interpretation in terms of pairs of primes both of which are 6 away from another prime, but which are not necessarily 6 apart themselves). If (4), well, _what_ else?

Harry, could you be more explicit about _why_ you might want to talk about sexy primes without using the term "sexy primes"?

My apologies for being dim.

--
g

[Allan Wechsler]

Perhaps Harry is just concerned about whether he is allowed to assume that the reader knows what "sexy prime" means, when writing explanatory text, or whether he needs to spell it out. An analogy: suppose for some reason we wanted to archive the sequence 1, 2, 5, 11, 90, ... of the integer square roots of Mersenne primes. (No, I am not nominating this sequence. (Why not? Interesting question, for another post.)) Could we title this sequence "Integer square roots of Mersenne primes"? Or are we encouraged to say, "Integer square roots of primes of the form 2^k - 1"? Harry might just be asking this stylistic question about the term "sexy prime".

Of course I could be way off base and would be happy to be corrected by Harry.

-- Allan

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[Sean A. Irvine]

Maybe Harry's question is something like this:

Sexy primes come in pairs (5, 11), (7, 13), etc.

Now suppose you want to refer to the pair ((5, 11), (7, 13)), how do you describe that?

Calling it a pair of sexy primes runs the risk of misinterpreting because sexy primes themselves come in pairs.

Sean.

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[M F Hasler]

I am still not very sure whether the problem is the word "sexy" 

(which comes from latin "sex" for 6, so : just don't worry about this, 

let's say, to simplify, it's "perfectly scientific" terminology)

or the confusion about a pair of primes from distinct "sexy pairs", 

say (p, p+6) and (q, q+6). 

Then it's actually not specific to those. The same arises for pairs of primes which could be, 

each one "individually", member of a (distinct) pair of twin primes, 

or "cousin primes" or whatever -- even a pair of Mersenne primes [which would be less confusing, though].)

Clearly, we can have pairs of "xx primes" which do not form an xx prime pair, for many different xx. 

For example, since 11 is a (lesser) twin prime, and 17 is also a (lesser) twin prime, technically (11, 17) is a pair of twin primes,

(i.e., primes that are members of a twin prime pair) but it's clearly not what we call a twin prime pair.

Similarly, one could have a pair of sexy primes (p,q) (each on it's own a member of a sexy pair), but which would *not* form a sexy (prime) pair, because they don't satisfy q = p+6.

Now, the problem could be still elsewhere:

is it about primes  p, q  such that q = p + 6, but there's a prime  (p+2 or p+4=q-2) between  p and q ?

(I thought we would not call those a sexy prime pair.  But to my surprise, I was wrong:

For example (5,11) is obviously considered a sexy prime pair in OEIS (cf. A023201 and A046117)

although there is 7 between the two. The Wikipedia page https://en.wikipedia.org/wiki/Sexy_primes

also explicitly considers that case and says that those are "part of a prime triplet". 

[just quoting what's written there, no need to tell me "triplets are babies, three numbers form a triple" !]

and Eric W's "MathWorld" also agrees on that.

(He also speaks of "sexy triplets" for 3 primes (p, p+6, p+12), though...)

Now I guess the problem could be still another one... For example :

On Thu, Dec 4, 2025 at 4:03 PM Sean A. Irvine <sai...@gmail.com> wrote:

Now suppose you want to refer to the pair ((5, 11), (7, 13)), how do you describe that?

I guess it's completely clear that here we do have (and should talk about) a pair of sexy prime pairs.

But again, that's not specifically related to sex, the latin word for 6.

It's quite funny how long such a question may remain unclear!

- Maximilian

[Daniel Mondot]

Perhaps you might consider the wording:

(5,11) is a paired pair of sexy primes, and so is (7,13).

While (5,13) is an unpaired pair of sexy primes, while 5 and 13, are still sexy primes, individually.

D. 

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