Is the sequence of the sum of digits of prime numbers bounded? (Q428389)

The author considers (and solves some of them) various problems regarding, \(s_q(p)=\) sum of digits of the prime number \(p\) written in base \(q\). Particularly, he proves a general result, which specially implies that the sequence \(s_q(p))\), when \(p\) runs through the primes, is not bounded above. The author is not aware that, this result is due to \textit{W. Sierpiński} [Rend. Circ. Mat. Palermo, II. Ser. 10, 229--232 (1961; Zbl 0107.26407)]. (For related, and many properties of the function \(s_q(n)\), see the reviewer's and \textit{B. Crstici's} monograph [Handbook of number theory. II: Dordrecht: Kluwer Academic Publishers. 637 p. (2004; Zbl 1079.11001)]).