Excel in math, science, and engineering
Form a cycle with a permutation of the first \(n\) positive integers. The cycle is called Prime Cycle if all neighboring pairs sum up to be a prime. The two distinct prime cycles for \(n=6\) are:
The permutation \(3,2,5,6,1,4\) is considered the same as the first sequence.
How many distinct prime cycles are there for \(n=16\)?