In number theory, the Bateman-Horn conjecture is a vast generalization of such conjectures as the Hardy and Littlewood conjecture on the density of twin primes or their conjecture on primes of the form n2+1; it is also a strengthening of Schinzel's hypothesis H.
It provides a conjectured density for the condition that all of a set of polynomials evaluated at a positive integer give a prime number. The set of polynomials 
are m distinct, irreducible polynomials with integer coefficients, such that the leading coefficients are positive and such that if f is the product of all the polynomials fi, then there does not exist a prime number p dividing f(n) for every positive integer n. If P(x) is the number of positive integers less than x such that all of the polynomials evaluate to a prime, then the conjecture is
where C is the product over primes p
with N(p) the number of mod p solutions to 
where f is the product of the polynomials fi, and D is the product of the degrees of the polynomials, or in other words the degree of f.
References
Bateman, P. T. and Horn, R. A., A heuristic asymptotic formula concerning the distribution of prime numbers, Mathematics of Computation 16 (1962), pp 363-367