The smallest prime whose reversal is a cube. [Honaker]
The first successful identification of a Mersenne prime by means of electronic digital computer was achieved in the year 1952, using the U.S. National Bureau of Standards Western Automatic Computer (SWAC) at the Institute for Numerical Analysis at the University of California, Los Angeles. It was M(521).
The largest known Mersenne prime exponent of the form (2^(2^k + 1)) + 2^k + 1. [Luhn]
521 is the sum of two squares (112 + 202). Note that 11 + 20 is a Mersenne prime exponent as well. [Luhn]
521 is the smallest Mersenne prime exponent that exceeds the sum of all smaller ones. [Terr]
521 is the reversal of 5^(2+1). [Post]
If p is prime, then it divides the pth term of the Perrin sequence: 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, ... (each term is the sum of the two terms preceding the term before it). Often, if n > 1 divides the nth term, then n is prime. The first of infinitely many exceptions to this rule is the square of 521. There are only 17 such composites less than 10^9.
The smallest prime p that has exactly one single-digit gap between p and a larger prime. [Honaker]
(There are 8 curios for this number that have not yet been approved by an editor.)