An Eisenstein prime with no imaginary part.
The smallest conductor of a rank 2 elliptic curve.
The smallest emirp equal the sum of the first two dozen consecutive idoneal numbers. [Loungrides]
The first in the smallest set of 4 consecutive primes (389, 397, 401, 409) that are congruent to 1 (mod 4). [Post]
The emirp whose common logarithm first exceeds its prime digital root. [Beedassy]
The smallest prime (emirp) whose sum of digits is an abundant number. [Loungrides]
(There are 5 curios for this number that have not yet been approved by an editor.)