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...