 With the exceptions of (2, 3, 5) and (3, 5, 7), this is the closest possible grouping of three prime numbers, since one of every three sequential odd numbers is a multiple of three, and hence not prime (except for 3 itself).The first prime triplets are

A prime triplet contains a pair of twin primes ("p" and "p" + 2, or "p" + 4 and "p" + 6), a pair of cousin primes ("p" and "p" + 4, or "p" + 2 and "p" + 6), and a pair of sexy primes ("p" and "p" + 6).A prime can be a member of up to three prime triplets - for example, 103 is a member of (97, 101, 103), (101, 103, 107) and (103, 107, 109).