A hierarchy of double, quadruple and octuple primes

In this paper double, quadruple and octuple primes are discussed. Computational and theoretical properties as well as examples of quadruple and octuple primes are presented, where the octuple primes in most cases have primes between the defining quadruples although the existence of a pure quadruple prime has also been demonstrated computationally. The possibility of sixtentuple primes is also briefly discussed.