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Erastosthenes (276 - 196 B.C.)

Eratosthenes invented a method for efficiently constructing
tables of prime numbers. This method, the "Sieve of
Eratosthenes", It goes like this. First, write down a list
of integers beginning with 2 and ending with some number, say,
20:
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Then mark all multiples of 2:
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
x x x x x x x x x

Move to the next unmarked number, which in this case is 3, then
mark all its multiples:
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
x x x x x x x x x x x

Continue in this fashion, marking all multiples of the next
unmarked number until there are no new unmarked numbers. The
final result is in fact the last table given, so the primes not
exceeding 20 are
2 3 5 7 11 13 17 19