A set of three prime numbers which form an arithmetic sequence with common difference two is called a prime triplet.
An example of a prime triplet is .
turns out to be the only prime triplet. This is because any set becomes , , or . Therefore in every triplet there exists one number that is divisible by . The only prime number divisible by is itself, so the only triplets possible are and . Since is not a prime, is the only prime triplet.