# prime gap

## Polignac's Conjecture โ โ โ

Author(s): de Polignac

\begin{conjecture} Polignac's Conjecture: For any positive even number n, there are infinitely many prime gaps of size n. In other words: There are infinitely many cases of two consecutive prime numbers with difference n. \end{conjecture}

In particular, this implies:

\begin{conjecture} Twin Prime Conjecture: There are an infinite number of twin primes. \end{conjecture}