What is Friedlander–Iwaniec theorem?

In analytic number theory the Friedlander–Iwaniec theorem states that there are infinitely many prime numbers of the form a 2 + b 4 {\displaystyle a^{2}+b^{4}}. 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 a 2 + b 4 {\displaystyle a^{2}+b^{4}} less than X {\displaystyle X} is roughly of the order X 3 / 4 {\displaystyle X^{3/4}}.