it is a famous conjecture that any one variable polynomial satisfying some simple conditions should take infinitely many prime values. unfortunately, this isn't known in any case except for linear polynomials - the sparsity of values of higher degree polynomials causes substantial difficulties. if we look at polynomials in multiple variables, then there are a few polynomials known to represent infinitely many primes whilst still taking on `few' values; friedlander-iwaniec showed $x^2+y^4$ is prime infinitely often, and heath-brown showed the same for $x^3+2y^3$. we will demonstrate a family of multivariate sparse polynomials all of which take infinitely many prime values.