Type: Article
Publication Date: 1962-01-01
Citations: 270
DOI: https://doi.org/10.1090/s0025-5718-1962-0148632-7
Suppose fi, f2, -*, fk are polynomials in one variable with all coefficients integral and leading coefficients positive, their degrees being hi, h2, **. , hk respectively. Suppose each of these polynomials is irreducible over the field of rational numbers and no two of them differ by a constant factor. Let Q(fi , f2, ... , fk ; N) denote the number of positive integers n between 1 and IV inclusive such that fi(n) , f2(n), , fk(n) are all primes. (We ignore the finitely many values of n for which some fi(n) is negative.) Then heuristically we would expect to have for N large