Yin-Dong He

A Monic Cubic Polynomial Generating 40 Consecutive Prime Values, Counted by Absolute Value

We prove that the monic cubic polynomial\(P(n) = n^3 + 54n^2 - 2917n + 20021\)has the following properties: \(|P(n)|\) is prime for every integer \(n\) with\(0 \le n \le 39\), and \(P(40) = 53741\) is composite. The forty values containexactly thirty-nine distinct primes, since \...

A Monic Cubic Polynomial Generating 40 Consecutive Prime Values, Counted by Absolute Value

We prove that the monic cubic polynomial\(P(n) = n^3 + 54n^2 - 2917n + 20021\)has the following properties: \(|P(n)|\) is prime for every integer \(n\) with\(0 \le n \le 39\), and \(P(40) = 53741\) is composite. The forty values containexactly thirty-nine distinct primes, since \...