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Description

1)

Alice has an even number of N beads, and each bead has a number from 1 to N painted on it. She would like to make a necklace out of all the beads, with a special requirement: any two beads next to each other on the necklace must sum to a prime number. Alice needs your help to calculate how many ways it is possible to do so.

`For example:`

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`N = 4`

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`There are two possible ways to build the necklace. Note that the last bead connects to the first bead.`

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`1 2 3 4`

`1 4 3 2`

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`Note: The necklace should be unique. For example: 1 2 3 4 is the same as 2 3 4 1 and 3 4 1 2 and 4 1 2 3`

`2)`

Reverse and Add Function

The reverse and add function starts with a number, reverses its digits, and adds the reverse to the original. If the sum is not a palindrome, repeat this procedure until it does.

Write a program that takes number and gives the resulting palindrome (if one exists). If it took more than 1,000 iterations (additions) or yield a palindrome that is greater than 4,294,967,295, assume that no palindrome exist for the given number.