Resumen de Prime-generating quadratic polynomials

Víctor Julio Ramírez Viñas

• Let a, b, c be integers. We provide a necessary condition for the function |ax2 + bx + c| to generate only primes for consecutive integers. We then apply this criterion to give sufficient conditions for the real quadratic field K = Q(√d), d ∈ N, to have class number one, in terms of prime-producingquadratic polynomials.