A prime triplet contains a pair of twin primes (p and p + 2, or p + 4 and p+ 6), a pair of cousin primes (pand p + 4, or p + 2 and p + 6), and a pair of sexy primes (p and p + 6).
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Apart from (2, 3, 5) and (3, 5, 7), they are Prime number of the from (p, p+2, p+6) or (p, p+4, p+6).