# Find the Good Number

Level pending

$$M$$ 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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