# Prime Cycle

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:

• $$1,4,3,2,5,6$$
• $$1,6,5,2,3,4$$

The permutation $$3,2,5,6,1,4$$ is considered the same as the first sequence.

How many distinct prime cycles are there for $$n=16$$?

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