A prime is a natural number greater than one whose only factors are one and itself. I find primes pretty cool, so I made a list of 50 facts about primes:

- The first twenty primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71.
- For any positive natural number $n$, there is always a prime between $n$ and $2n$. This is known as Bertrand's postulate.
- A Mersenne prime is a prime of the form $2^n – 1$. Such a number is prime if and only if $2^{n-1}(2^n-1)$ is a perfect number (a number equal to the sum of all its proper divisors). All even perfect numbers arise this way, and no one knows if an odd perfect number exists.
- There are 51 known Mersenne primes, and it is unknown whether there are infinitely many.
- The largest prime that humans have ever found is $2^{82,589,933}-1$ and is a Mersenne prime. It was discovered in 2018.
- It is pretty easy to come up with a new kind of prime, such as a "palindromic prime", but most of the time it is very difficult to prove that there are infinitely many such primes. In case you're curious, 142840628019121910826048241 is a palindromic prime.