Unsolved Problems

Let $a_1, \ldots, a_k$ be given integers. Then there exist infinitely many positive integers $n$ such that $n + a_1, \ldots, n + a_k$ are all prime, p...

For all integers $x, y \geq 2$, we have $\pi(x+y) \leq \pi(x) + \pi(y)$, where $\pi(n)$ denotes the prime counting function (the number of primes less...

For a polynomial $f(x) = ax^2 + bx + c$ with $a > 0$, $\gcd(a,b,c) = 1$, and discriminant $\Delta = b^2 - 4ac$ not a perfect square, the polynomial ta...