Bi-twin chain

In number theory, a bi-twin chain of length k + 1 is a sequence of natural numbers in which every number is prime.

[1] The special case, when the four numbers

are all primes, they are called bi-twin primes,[2] such n values are Except 6, all of these numbers are divisible by 30.

form a Cunningham chain of the first kind of length

forms a Cunningham chain of the second kind.

is a pair of twin primes.

is a safe prime.

q# denotes the primorial 2×3×5×7×...×q.

As of 2014[update], the longest known bi-twin chain is of length 8.