Apart from {2,3,5} and {3,5,7} prime triplets are sets of the from {n, n+2, n+6} or {n, n+4, n+6} such that each of the three numbers in the set are primes.
Note that {n, n+2, n+4}, three alternate [odd] numbers cannot all be primes since one of them must be divisible by 3.
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3,5,7 is the only prime triplet.
From Wikipedia ("Prime triplet"): "Similarly to the twin prime conjecture, it is conjectured that there are infinitely many prime triplets." So, it seems that nobody really knows for sure. "It is conjectured" means that it seems reasonable to suppose that there are infinitely many, but that it hasn't been proven yet.
the sides of a triangle on which the Pythagorean theorem can be applied is called Pythagorean triplet
She gave birth to triplets.
A triplet.