Every prime is the smallest quadratic nonresidue for infinitely many primes

Statement

Suppose $p$ is a prime number. Then, there exist infinitely many primes $q$ such that $p$ is the smallest quadratic nonresidue modulo $q$.

Related facts

• Every prime p is a p-adic nonresidue for some prime
• Every prime p is a p-adic nonresidue for infinitely many primes
• Every integer is a quadratic residue for infinitely many primes
• Every integer that is not a perfect square is a quadratic nonresidue for infinitely many primes