Let $P(n): n$ and $n+2$ are primes. be an open sentence over the domain N. Find six positive integers $n$ for which $P(n)$ is true. If $n \in \mathbf{N}$ such that $P(n)$ is true, then the two integers $n, n+2$ are called twin primes. It has been conjectured that there are infinitely many twin primes.