11047
This number is a prime.
Conjectured to be the smallest positive integer k such that
(k*3^n+1)/gcd(k+1,3-1) is composite for all integers
n>=1. [Luen]
By the 1338th prime number (11047) there are 669 primes
with distinct digits and 669 primes with at least two of
the same digit. This is the first and probably only case in
which the two counts are equal. [Gaydos]
The smallest Cyclops prime containing all straight digits. [Gupta]
(There are 4 curios for this number that have not yet been approved by an editor.)
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