Friedlander–Iwaniec theorem


In analytic number theory the Friedlander–Iwaniec theorem states that there are infinitely many prime numbers of the form. 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 less than is roughly of the order.

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.

Special case

When, the Friedlander–Iwaniec primes have the form, forming the set
It is conjectured that this set is infinite. However, this is not implied by the Friedlander–Iwaniec theorem.