Smallest Prime with Prime Sum

Given an integer \(n\), your task is to find the smallest prime number \(p\) such that both \(p\) and \(p+n\) are prime numbers. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example, when \(n = 10\), the number \(3\) is the smallest prime since both \(3\) and \(3+10=13\) are primes.

More formally, find the minimum prime \(p\) satisfying:

[ \text{is_prime}(p) = \text{True} \quad \text{and} \quad \text{is_prime}(p+n) = \text{True} ]

inputFormat

The input consists of a single line containing one integer \(n\) (for example, \(0 \leq n \leq 1000\)).

outputFormat

Output a single integer: the smallest prime number \(p\) such that both \(p\) and \(p+n\) are prime numbers.

10

3