Friedlander–Iwaniec theorem
In analytic number theory the Friedlander–Iwaniec theorem states that there are infinitely many prime numbers of the form formula_1. The first few such primes are The difficulty in this statement lies in the very sparse nature of this sequence: the number of integers of the form formula_2 less than formula_3 is roughly of the order formula_4. History. The theorem was proved in 1997 by John Friedlander and Henryk Iwaniec. Iwaniec was awarded the 2001 Ostrowski Prize in part for his contributions to this work. Refinements. The theorem was refined by D.R. Heath-Brown and Xiannan Li  in 2017. In particular, they proved that the polynomial formula_1 represents infinitely many primes when the variable formula_6 is also required to be prime. Special case. When , the Friedlander–Iwaniec primes have the form formula_7, forming the set It is conjectured (one of Landau's problems) that this set is infinite. However, this is not implied by the Friedlander–Iwaniec theorem.