The polynomials X2+(Y2+1)2$X^2+(Y^2+1)^2$ and X2+(Y3+Z3)2$X^{2} + (Y^3+Z^3)^2$ also capture their primes

Abstract We show that there are infinitely many primes of the form and . This extends work Friedlander Iwaniec showing More precisely, obtained an asymptotic formula for number this form. For sequences , we establish Type II information is too narrow aysmptotic formula, but can use Harman's sieve method to produce a lower bound correct order magnitude Estimating sums reduced counting problem solved by using Weil bound, where arithmetic input quite different from also represented incomplete norm degree with variables. this, require Deligne‐type correlations hyper‐Kloosterman sums.