Why is Sieve of Eratosthenes more efficient than the simple “dumb” algorithm?

Question

If you need to generate primes from 1 to N, the \"dumb\" way to do it would be to iterate through all the numbers from 2 to N and check if the numbers are divisable by any p

Answer 1

Explained in this paper: http://www.cs.hmc.edu/~oneill/papers/Sieve-JFP.pdf

I think it's quite readable even without Haskell knowledge.