A pair of primes is called SEXY when their difference is equal to 6.

The name sexy comes from the Latin word "sex": six

The first 3 pairs are (5,11) (7,13) (11,17)

The first 3 triplets are:
(5,11,17) (17,23,29) (31, 37, 43)

Only a set of five exists: it is
(5,11,17,23,29)