Do You Like "Odd" Primes?

Number Theory Level 5

Let \(P\) denote the set of odd primes under 1000. \(p\) is an element of \(P\) that satisfies the following:

For any \(S=\{p_1,p_2,\ldots,p_k\}\subseteq P\) where \(k\ge 2\) and \(p_i\ne p\) for \(i=1,2,\ldots,k\), there exists \(q\in P\backslash S\) such that


Find the sum of all possible \(p\).


Problem Loading...

Note Loading...

Set Loading...