Abstract
In this paper, we look at numbers of the form H-r,H-k := Fk-1Fr-k +2 + FkFr-k. These numbers are the entries of a triangular array called the determinant Hosoya triangle which we denote by H. We discuss the divisibility properties of the above numbers and their primality. We give a small sieve of primes to illustrate the density of prime numbers in H. Since the Fibonacci and Lucas numbers appear as entries in H, our research is an extension of the classical questions concerning whether there are infinitely many Fibonacci or Lucas primes. We prove that H has arbitrarily large neighbourhoods of composite entries. Finally we present an abundance of data indicating a very high density of primes in H.