8191

This number is a prime.

The first comment from Bateman comes from the Goormaghtigh conjecture: the only two non-trivial integer solutions of the exponential Diophantine equation (x^m-1)/(x-1) = (y^n-1)/(y-1) with x > y > 1 and m,n > 2 give primes 31 and 8191, with here 8191 = (90^3-1)/89 = (2^13-1)/1 and 8191 = 111_90 = 1111111111111_2. So, 8191 is one of the only two primes to be Brazilian in two distinct bases, the second is 31. [Schott]