Friedlander–Iwaniec theorem

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

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