566 = 2 x 283.
566 is the number of ways to place 24 points on a 12 x 12 grid so that no three points are on a line (A000769).
The sum of the fourth power of the prime factors of 566 is a prime (A134620): 24 + 2834 = 6414247937, a prime.
566 is the sum of five distinct pentatope numbers (A104395).
566 is the sum of the first 20 primes minus the next prime (A166448).
Source: What's Special About This Number?