11

This number is a prime.

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The Klein cubic threefold is the only smooth cubic threefold which has an automorphism of order 11. [Post]

The smallest counterexample to Mersenne's conjecture is the Mersenne number M(11) = 2^11 - 1 = 2047 = 23 * 89, which is a semiprime (and brilliant) rather than a prime, even though 11 is a prime. [Post]