Almost primes represented by quadratic polynomials
Let G(x) be an irreducible polynomial with integer coefficients. It is conjectured that the set {n N G(n) is prime} is infinite for most G(x) If Pr denotes the set of squarefree positive integers with at most r prime factors, we consider the set {n N G(n) Pr} with the goal of showing that it is infinite for a suitable choice of r. Considerable work has been done on this problem, with the most notable results being due to Iwaniec, Buhstab, and Richert. Here we show that if deg(G(x) 2, then we may take r 2.