27611

This number is a prime.

In 1990, Balog proved there are arbitrarily large sets of primes for which the means of each pair of entries is a distinct prime. For example,

{71, 1163, 1283, 2663, 4523, 5651, 9311, 13883, 13931, 14423, 25943, 27611}

Granville believes there may be sets like this of infinite length!