Avoid Primes

You are given an integer $N$ and must construct a permutation $P$ of integers $[1, N]$. You define $f(P)$ as the number of integers $i$ ($1 \le i < N$) such that $\min(P_i, P_{i + 1})$ is prime. Note that $1$ is not considered a prime integer. For example, $f([4, 2, 1, 6, 5, 3]) = 3$ because $i = 1, 4, 5$ satisfies the condition. Find a permutation with minimum value of $f(P)$. If multiple permu