Find the Good Number

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\(M\) is the set of squares of the first \(20\) natural numbers:

\(M={1^2,2^2,3^2,4^2,\dots ,20^2}\).

We say that \(n\) is a good number, if in any subset of \(M\) of size \(n\) there are two elements, \(a\) and \(b\), such that \(a+b\) is a prime number. Find the smallest good number.

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