Prime numbers

Numbers bigger than 1 whose only factors are 1 and themselves - the numbers whose dots make only a single line, never a rectangle.

Depth 1 · Foundation

You can tell a prime from a composite number, know why 1 is neither, and find the primes up to 100 with the sieve of Eratosthenes.

Depths of understanding

1
Foundation
You can tell a prime from a composite number, know why 1 is neither, and find the primes up to 100 with the sieve of Eratosthenes.
Opens after
FactorsA prime is a number with exactly two factors, 1 and itself.
2
Deeper
You can follow Euclid's argument that the primes never run out - multiply the primes you have and add 1 - and say exactly what it proves.
Master depth 1 first
Mathematical proofThat the primes never run out is not something you can check; it has to be proved.Proof by contradictionEuclid's argument starts by supposing there is a last list of primes, and shows that leads to something impossible.

What's still between you and Prime numbers, depth 1, in the order you can learn it.