Prime numbers in the decimal system. (English) Zbl 0916.11005
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 \(S(p)= k\).
Reviewer: J.Piehler (Merseburg)