Let \(S(p)\) be the sum of the digits of the prime number \(p\). Then it is shown that \(S(p)\) is only divisible by 3 in the case \(p=3\). It is conjectured that for any integer \(k\neq 3m\), \(m= 2,3,4,\dots\) there exists at least one prime \(p\) for which \(S(p)= k\).