Demon

Input: an integer n > 1
 
Let A be an array of Boolean values, indexed by integers 2 to n,
initially all set to true.
 
for i = 2, 3, 4, ..., while i ≤ n/2:
  if A[i] is true:
    for j = 2i, 3i, 4i, ..., while j ≤ n:
      A[j] = false
 
Now all i such that A[i] is true are prime.
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