The Bateman-Horn Conjecture gives an asymptotic estiamte to the density of primes in the output of a polynomial. If Q(f; x) is the number of n ≤ x such that f(n) is prime, the Bateman-Horn Conjecture predicts that Q(f; x) is asymptotically equivalent to a certain constant times the offset logarithmic integral Li(x). My honors project involved exploring what the Bateman-Horn Conjecture predicts for the polynomial x2 + x + k. This repository contains a pair of Sage notebooks that allow the user to:
- Compute the constant C(f) for f(x) = x2 + x + k
- Plot the prediction made by the Bateman-Horn Conjecture vs. the actual count of the primes.