Sexy primes are pairs of primes of the form (
, 
),
so-named since "sex" is the Latin word for "six.". The first
few sexy prime pairs are (5, 11), (7, 13), (11, 17), (13, 19), (17, 23), (23, 29),
(31, 37), (37, 43), (41, 47), (47, 53), ... (OEIS A023201
and A046117). As of November 2005, the largest
known sexy prime pair starts with
![p={48011837012[(53238·7879#)^2-1]+2310}·(53238·7879#)/(385)+1,](/images/equations/SexyPrimes/NumberedEquation1.svg) |
(1)
|
where 
is a primorial.
These primes have 10154 digits and were found by M. Fleuren, T. Alm, and
J. K. Andersen (Andersen 2005).
Sexy constellations also exist. The first few sexy triplets (i.e., numbers such that each of 
is prime but 
is not prime) are
(7, 13, 19), (17, 23, 29), (31, 37, 43), (47, 53, 59), ... (OEIS A046118,
A046119, and A046120).
As of October 2005, the largest known sexy triplet starts with
 |
(2)
|
These primes have 5132 digit digits and were found by Davis (2005).
The first few sexy quadruplets are (11, 17, 23, 29), (41, 47, 53, 59), (61, 67, 73, 79), (251, 257, 263, 269), ... (OEIS A023271, A046122, A046123, and A046124). Sexy quadruplets can only begin with a prime ending in a "1." As of November 2005, the largest known sexy quadruplet starts with
 |
(3)
|
These primes have 1002 digits and were found by J. K. Andersen (2005).
There is only a single sexy quintuplet, (5, 11, 17, 23, 29), since every fifth number of the form 
is divisible by 5, and therefore cannot be prime.
