Counting Primes whose Sum of Digits is Prime
Department of Mathematics
Royal Holloway, University of London
Surrey TW20 0EX
Motivated by recent work of Drmota, Mauduit and Rivat, we discuss the
possibility of counting the number of primes up to x whose sum of
digits is also prime. We show that, although this is not possible
unless we assume a hypothesis on the distribution of primes stronger
than what is implied by the Riemann hypothesis, we can establish a
Mertens type result. That is, we obtain a formula for the number of
such primes p up to x weighted
with a factor 1/p. Indeed, we can iterate the method and count
primes with the sum of digits a prime whose sum of digits is a prime,
and so on.
Full version: pdf,
(Concerned with sequences
Received September 16 2011;
revised version received December 29 2011.
Published in Journal of Integer Sequences, December 30 2011.
Journal of Integer Sequences home page