# 521

This number is a prime.

The smallest prime number whose reversal is a cube. Curiously, its sum of digits equals the smallest prime cubed. [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 (11^{2} + 20^{2}).
Note that 11 + 20 is a Mersenne prime exponent as well. [Luhn]

*M*(521) can be written as 512*2^{512} - 1. Therefore, it is a Woodall prime as well as a Mersenne prime. [Dobb]

521 is the smallest Mersenne prime exponent that exceeds the sum of all smaller ones. [Terr]

The lesser prime of the only pair of twin primes less than one thousand for which their cubes, when reversed, form primes. [Trotter]

521 is the reversal of 5^(2+1). [Post]

If *p* is prime, then it divides the *p*th 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 *n*th 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 of the form p=2^n+n for n a composite integer (n=9). [Loungrides]

A year consists of 52 weeks and 1 day. [Gudipati]

Largest known Lucas number n such that 2^n-1 is prime. [Luen]

The sum of the squares of three consecutive semiprimes starting at (5*2*1) is 521. [Worrom]