Prime triplet
A set of three prime numbers which form an arithmetic sequence with common difference two is called a prime triplet.
Discussion
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 1 is not a prime,
is the only prime triplet.