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Counting Primes whose Sum of Digits is Prime
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Glyn Harman

Department of Mathematics

Royal Holloway, University of London

Egham

Surrey TW20 0EX

United Kingdom

**Abstract:**

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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