Geodesic
Integer sequences avoiding prime pairwise sums
Journal of integer sequences, Tome 11 (2008) no. 5
The following result is proved: If $A\subseteq \{ 1,\, 2,\, \ldots ,\, n\} $ is the subset of largest cardinality such that the sum of no two (distinct) elements of $A$ is prime, then $\vert A\vert=\lfloor(n+1)/2\rfloor$ and all the elements of $A$ have the same parity. The following open question is posed: what is the largest cardinality of $A\subseteq \{ 1,\, 2,\, \ldots ,\, n\} $ such that the sum of no two (distinct) elements of $A$ is prime and $A$ contains elements of both parities?
Keywords: primes, sumsets, distribution of primes 
@article{JIS_2008__11_5_a1,
     author = {Chen,  Yong-Gao},
     title = {Integer sequences avoiding prime pairwise sums},
     journal = {Journal of integer sequences},
     year = {2008},
     volume = {11},
     number = {5},
     zbl = {1196.11042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2008__11_5_a1/}
}
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Chen,  Yong-Gao. Integer sequences avoiding prime pairwise sums. Journal of integer sequences, Tome 11 (2008) no. 5. http://geodesic.mathdoc.fr/item/JIS_2008__11_5_a1/