Is it always possible to demonstrate the existence of at least one prime number of the form 2 + pq, where p is an arbitrarily large prime number and q is a prime number greater than p?
Other word, if I pick a prime number p, must there exist at least one prime number of a form 2+pq, while q is bigger prime number than p? I know there exist infinitely many of the form 2+np where n is integer (according to Dirichlet theorem) but I wonder if the stated sentence is true too