Polynomials whose reducibility is related to the Goldbach conjecture
  We introduce a collection of polynomials $F_N$, associated to each positive integer $N$, whose divisibility properties yield a reformulation of the Goldbach conjecture. While this reformulation certainly does not lead to a resolution of the conjecture, it does suggest two natural generalizations for which we provide some numerical evidence. As these polynomials $F_N$ are independently interesting, we further explore their basic properties, giving, among other things, asymptotic estimates on the growth of their coefficients. 
Peter B. Borwein, Stephen K.K. Choi, Greg Martin, Charles L. Samuels
math.NT