Problem C

Just Sum Primes

A *prime number* is an integer greater than \(1\) that has only two positive divisors: \(1\) and itself. The number \(17\) is prime because its only positive divisors are \(1\) and \(17\).

The variables \(a\), \(b\), \(c\), and \(d\) represent four different prime numbers. If \(a\times b\times c\times d\) is equal to a three-digit number with a tens digit of \(1\) and a ones (units) digit of \(0\), determine all the possible values of \(a+b+c+d\).

**Theme:** Number Sense