# Problem 574: Verifying Primes
Let \$q\$ be a prime and \$A \\ge B >0\$ be two integers with the
following properties: \$A\$ and \$B\$ have no prime factor in common,
that is \$\\text{gcd}(A,B)=1\$. The product \$AB\$ is divisible by every
prime less than q. It can be shown that, given these conditions, any sum
\$A+B