🔢 Perfect Numbers Network

Join the distributed search for perfect numbers

Download & Start Computing

What are Perfect Numbers?

A perfect number is a positive integer that equals the sum of its proper divisors (excluding itself). These rare mathematical gems have fascinated mathematicians for over 2,000 years!

First Perfect Number: 6

Divisors of 6: 1, 2, 3

Sum: 1 + 2 + 3 = 6 ✨

Second Perfect Number: 28

Divisors of 28: 1, 2, 4, 7, 14

Sum: 1 + 2 + 4 + 7 + 14 = 28 ✨

Third Perfect Number: 496

Divisors of 496: 1, 2, 4, 8, 16, 31, 62, 124, 248

Sum: 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496 ✨

Euclid-Euler Theorem

Every even perfect number can be represented as:

Perfect Number = 2p-1 × (2p - 1)

where 2p - 1 is a Mersenne prime

This elegant formula, discovered by Euclid and proven complete by Euler, connects perfect numbers to Mersenne primes. Finding Mersenne primes allows us to generate new perfect numbers!

Why Join This Project?

🔍

Mathematical Discovery

Help discover new perfect numbers that humanity has never seen before

🌐

Distributed Computing

Join a global network of computers working together

📚

Learn & Contribute

Understand number theory, algorithms, and distributed systems

🏆

Credit & Recognition

Get credited for your computational contributions

Known Perfect Numbers

51
Known Perfect Numbers
24.8M
Digits in Largest
2,300+
Years of Study

The largest known perfect number has 49,724,095 digits and was discovered in 2018!

How It Works

  1. Download the client software for your platform
  2. Run the client and choose a username
  3. Receive work assignments from the server
  4. Compute using the Lucas-Lehmer test algorithm
  5. Submit results and help discover perfect numbers!

Ready to Start?

Download the software and join the search for perfect numbers!

Get Started Now