# A Prime Quadratic

**Number Theory**Level 5

Let \(S\) be the set of all ordered triples \((p,q,r)\) of prime numbers for which at least one rational number \(x\) satisfies \(px^2+qx+r=0\). Find all the primes that appear in seven or more elements of \(S\)?

Enter your answer as the sum of all such primes.

Enter 0 if there is no such prime.