Prime-generating polynomial
Statement
An irreducible polynomial f with integer coefficients, positive leading coefficient, and gcd(f(1), f(2), f(3), ...) = 1 takes prime values for infinitely many positive integers n. Euler's polynomial n² + n + 41 produces 40 primes for n = 0, 1, ..., 39.
Proposed: 1857
Proposer: Viktor Bunyakovsky