There are infinitely many primes of the form x^3+2y^3

You need to know: Prime numbers.

The Theorem: On 29th April 1999, Rodger Heath-Brown submitted to Acta Mathematica a paper in which he proved that there are infinitely many primes of the form $x^3+2y^3$ with integer x, y.

Short context: Let P be a polynomial with integer coefficients in one or more variables. If we substitute integer values instead of variables, will we get infinitely many primes as values of P? This problem is wide open even for simple polynomials like $P(x)=x^2+1$ . Famous Dirichlet’s theorem solves it for linear polynomials, Iwaniec in 1974 resolved the case of quadratic polynomials in 2 variables (which depends essentially on both variables), while Friedlander and Iwaniec proved in 1998 that there are infinitely many primes of the form $x^2+y^4$ with integer x, y. The Theorem resolves this question for polynomial $P(x,y)=x^3+2y^3$ .