A True Kurepa Conjecture Implies Dirichlet-Kurepa Primes: Two New Classes of Infinite Primes Within Arithmetic Progressions
Prashanth R. Rao · viXra · 2016
The Kurepa conjecture states that the gcd (!n,n!) is equal to 2 for all n=2,3,….Although this conjecture has not been proven, in this paper we study the implication of a true Kurepa conjecture. We use (!n)/2 and (n!)/2 as components of two distinct arithmetic progressions and propose that both should have infinitely many primes as known from Dirichlet’s theorem of Arithmetic progressions and these are named as Dirichlet-Kurepa primes Type 1 and Type 2 in their honor.