In the Simpsons, the following appeared on a Jumbo-tron:
The writers purposely selected a perfect number, a narcissistic number, and a prime number.
8191 is a mersenne prime number. (A prime number is a number that has exactly 2 factors - itself and 1. A mersenne prime is a prime number of the form 2^p-1, where p is a prime number. 8191 is 2^13 -1)
8128 is a perfect number. (A perfect number is a number that is equal to the sum of its proper factors. The proper factors of 8128 are 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064 and these add up to 8128.)
8208 is a narcissistic number. (A narcissistic number is a number that, if you raise each digit to the power of the number of digits you have, and add all of them, you get the original number. 8208 has 4 digits, and 8^4+2^4+0^4+8^4 = 8208.)