There's a simple combinatorial proof of the existence of a prime between n and n^2: https://www.quora.com/Is-there-a-prime-between-every-natural-number-greater

There's a simple combinatorial proof of the existence of a prime between n and n^2: https://www.quora.com/Is-there-a-prime-between-every-natural-number-greater-than-1-and-its-square https://www.quora.com/Is-there-a-prime-between-every-natural...