The newest perfect number discovered is 2<sup>82,589,933</sup> - 1. This number is massive, containing over 24 million digits!
Understanding Perfect Numbers
A perfect number is a positive integer that is equal to the sum of its proper divisors (the divisors excluding the number itself). For example, 6 is a perfect number because its proper divisors are 1, 2, and 3, and 1 + 2 + 3 = 6.
Finding Perfect Numbers
Perfect numbers are related to Mersenne primes. A Mersenne prime is a prime number that can be written in the form 2<sup>p</sup> - 1, where p is also a prime number. It has been proven that if 2<sup>p</sup> - 1 is a Mersenne prime, then 2<sup>p-1</sup>(2<sup>p</sup> - 1) is a perfect number.
The Importance of Perfect Numbers
While perfect numbers have no direct practical applications, they are fascinating mathematical objects that have intrigued mathematicians for centuries. Their study has led to the development of important mathematical concepts and algorithms.
The Search Continues
The discovery of new perfect numbers relies on finding new Mersenne primes. The Great Internet Mersenne Prime Search (GIMPS) is a distributed computing project that uses volunteers' computers to search for new Mersenne primes. As the search continues, we can expect to find even larger perfect numbers in the future.
