Journal of Integer Sequences, Vol. 15 (2012), Article 12.2.2

Counting Primes whose Sum of Digits is Prime

Glyn Harman
Department of Mathematics
Royal Holloway, University of London
Surrey TW20 0EX
United Kingdom


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.

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(Concerned with sequences A046704 A070027 A109981.)

Received September 16 2011; revised version received December 29 2011. Published in Journal of Integer Sequences, December 30 2011.

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