Prime permutations

A permutation $P$ of $\{1,2,\dots ,n\}$ is said prime if:

• $P_1=1$
• $P_n=n$
• $\mathrm{\forall }i<n,P_i+P_{i+1}$ is a prime number

$\{1,6,5,8,9,2,3,4,7,10\}$ is a prime permutation

How many prime permutations are there for $n=21$?

[My timing: 30 sec]