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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[Harry Neel]

Thanks to all for your input.

First, I would like to let everyone know that I am neither trying to avoid nor advocate using any particular way of referring to two primes that are six (6) apart. It was while examining sexy prime sequences that I saw a comment by Neil that the definition for "sexy prime" in webpage of 'Eric Weisstein's World of Mathematics, Sexy Primes' is unsatisfactory. OEIS sequence 'A046124' (see included link) is but one sequence with Neil's comment. 

https://oeis.org/A046124

In the LINKS portion of the sequence is:

Eric Weisstein's World of Mathematics, Sexy Primes. [The definition in this webpage is unsatisfactory, because it defines a "sexy prime" as a pair of primes.- N. J. A. Sloane, Mar 07 2021].

Simple thing first. "Why is the definition in the referenced webpage unsatisfactory?"

Simple thing second: "What is the (or a) satisfactory definition, and does it affect the way sexy primes are described in the naming or definition of sequences? From what I have seen the answer is either 'No' or 'Probably Not.'

If I read responses correctly, one response indicated that prime numbers can be sexy primes individually. Twenty-three (23) when associated with seventeen(17) forms (shall I say it) a sexy prime pair [pair of sexy primes; a couplet of sex primes; a dyad of sexy primes; a complement of sexy primes; a doublet of sexy primes; etc.] Twenty-three (23) and twenty-nine (29), likewise. By themselves they are only prime number with only themselves and one (1) as factors. Eleven (11) is not a twin unless PAIRED with thirteen (13).

And this 'thread' does not even get into the realm of isolated prime; that is the prime numbers 47 and 23 are isolated primes because there are no other prime numbers, p, that closer than p + 2, or p - 2.

I am way too far off subject.

[Harry Neel]

Thanks to all for your input.

First, I would like to let everyone know that I am neither trying to avoid nor advocate using any particular way of referring to two primes that are six (6) apart. It was while examining sexy prime sequences that I saw a comment by Neil that the definition for "sexy prime" in webpage of 'Eric Weisstein's World of Mathematics, Sexy Primes' is unsatisfactory. OEIS sequence 'A046124' (see included link) is but one sequence with Neil's comment. 

https://oeis.org/A046124

In the LINKS portion of the sequence is:

Eric Weisstein's World of Mathematics, Sexy Primes. [The definition in this webpage is unsatisfactory, because it defines a "sexy prime" as a pair of primes.- N. J. A. Sloane, Mar 07 2021].

Simple thing first. "Why is the definition in the referenced webpage unsatisfactory?"

Simple thing second: "What is the (or a) satisfactory definition, and does it affect the way sexy primes are described in the naming or definition of sequences? From what I have seen the answer is either 'No' or 'Probably Not.'

If I read responses correctly, one response indicated that prime numbers can be sexy primes individually. Twenty-three (23) when associated with seventeen(17) forms (shall I say it) a sexy prime pair [pair of sexy primes; a couplet of sex primes; a dyad of sexy primes; a complement of sexy primes; a doublet of sexy primes; etc.] Twenty-three (23) and twenty-nine (29), likewise. By themselves they are only prime number with only themselves and one (1) as factors. Eleven (11) is not a twin unless PAIRED with thirteen (13).

And this 'thread' does not even get into the realm of isolated prime; that is the prime numbers 47 and 23 are isolated primes because there are no other prime numbers, p, that closer than p + 2, or p - 2.

I am way too far off subject.

On Thursday, December 4, 2025 at 5:59:37 PM UTC-5 dmo...@gmail.com wrote:

[Arthur O'Dwyer]

On Fri, Dec 5, 2025 at 1:35 PM Harry Neel <neel...@gmail.com> wrote:

https://oeis.org/A046124

Eric Weisstein's World of Mathematics, Sexy Primes. [The definition in this webpage is unsatisfactory, because it defines a "sexy prime" as a pair of primes.- N. J. A. Sloane, Mar 07 2021].

Aha. FYI, this should have been the very first thing you said in your very first message.

Weisstein writes:

> Sexy primes are pairs of primes of the form (p, p+6) [...]

So indeed Neil's comment is correct: That definition is dumb, because no kind of prime is ever a pair of primes. That's just sloppy.

If we were inventing new terminology from scratch (which, unfortunately, we're not), I would suggest:

- Prime is an adjective applying to a number.

- Twin, cousin, and sexy are adjectives applying to a pair (or tuple) of numbers.

Then it would make sense to say

- (7,9) is a twin pair of integers.

- (4,8) is a cousin pair of powers of two. It is a cousin power-of-two pair.

- (5,11) is a sexy pair of primes. It is a sexy prime pair.

- (3,11,19,23) is an (unsexy) quadruple of primes.

- (5,11,17,23) is a sexy quadruple of primes. It is a sexy prime quadruple.

There would be no such thing as a "twin integer" or a "cousin power of two" or a "sexy prime number" in isolation.

But this rigorous/pedantic terminology can't be applied consistently in the real world, because we'd come across places that say "17 is a sexy prime," and it would be gratuitously annoying to rewrite that to "17 is one-half of a sexy pair of primes" or whatever. Also, in the case of sources like MathWorld, we can't rewrite the source (unless anyone has a connection at Wolfram?!) — so all we can do is comment on the unsatisfactoriness of their commentary and move on. Which is what Neil did in 2021.

–Arthur

[Harry Neel]

Arthur, et.al:

I completely agree that I did poorly in presentation in the beginning. Please forgive. I have attempted to clarify, again, poorly.

Yes, I left out a crucial aspect of the query in the beginning and only belatedly realized that had happened.

I will just call primes that are 6 apart sexy primes, a pair of sexy primes, pairs of sexy primes (when discussing two or more (pair, pairs, sets, doublets, [sorry, getting carried away] of sexy primes.)  

If I do so in an unsatisfactory way, I am sure that I will be informed.

Thank You All

Harry

[Allan Wechsler]

I think "a sexy prime pair" is brief and unambiguous. "A pair of sexy primes" is brief but has a potential ambiguity.

-- Allan

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