Journal of Integer Sequences, Vol. 11 (2008), Article 08.5.6 |

Department of Mathematics

Nanjing Normal University

Nanjing 210097

P. R. CHINA

**Abstract:**

The following result is proved: If
is the subset of largest cardinality such
that the sum of no two (distinct) elements of is prime, then
and all the elements of have the
same parity. The following open question is posed: what is the
largest cardinality of
such that the sum of no two (distinct) elements of is prime
and contains elements of both parities?

Received April 16 2008;
revised version received December 13 2008.
Published in *Journal of Integer Sequences*, December 13 2008.

Return to