Discover the fascinating world of perfect numbers
A perfect number is a positive integer that equals the sum of its proper divisors (excluding itself). In other words, if you add up all the factors of the number except the number itself, you get the number back.
Example 1: 6 has proper divisors 1, 2, and 3. 1 + 2 + 3 = 6 ✓
Example 2: 28 has proper divisors 1, 2, 4, 7, and 14. 1 + 2 + 4 + 7 + 14 = 28 ✓
Ancient Greek mathematician Euclid discovered that even perfect numbers follow a beautiful formula related to Mersenne primes:
Where (2p − 1) must be a prime number (called a Mersenne prime).
A Mersenne prime is a prime number that can be written in the form 2p − 1, where p itself is prime. Every Mersenne prime generates an even perfect number, and vice versa (for even perfect numbers).
While thousands of even perfect numbers have been discovered, no odd perfect number has ever been found. Mathematicians have proven many properties that odd perfect numbers must have, yet their existence remains one of the oldest unsolved problems in mathematics!