What are mersenne primes?

Mersenne primes are special kinds of prime numbers that follow a cool pattern.

Imagine you have a toy box where you can only keep toys that come in certain sizes. A Mersenne prime is like one of those special toys, it’s made by taking the number 2, and raising it to some power, then subtracting 1. If the result is a prime number, then it's a Mersenne prime!

For example, if you take $ 2^3 - 1 = 8 - 1 = 7 $, and 7 is a prime number (a number that only has 1 and itself as factors), then 7 is a Mersenne prime.

Think of it like baking cookies. You use a recipe with powers of 2:

• $ 2^2 - 1 = 3 $, also a prime!
• $ 2^5 - 1 = 31 $, that's another Mersenne prime!

People have been finding bigger and bigger Mersenne primes for centuries, like discovering the tallest tree in the forest. Some of them are super big, so big they can’t even be written down without using a calculator!