SIEVE OF ERATOSTHANES


Starting:
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To start the Sieve of Eratosthanes, write out all the numbers,
primes and composites alike, within a specified range, like.

2  3  4  5  6  7  8  9  10  11  12  13  14  15....




Continuing (Crossing-Out):
--------------------------

Then you cross out the ones divisible by 2 (except the first 2).

x  3  x  5  x  7  x  9   x  11   x  13   x  15....

Then you cross out the ones divisible by 3 (except the first 3).

2  3  x  5  x  7  x  X   x  11   x  13   x   X....
            X                    X           

Then you cross out the ones divisible by 5, then by 7,
et cetera, always choosing your next "cross-out number"
(like 2, 3, 5, 7, etc) by taking the first number in your 
sieve that has neither been a cross-out number, 
nor has been crossed out.




STOPPING:
---------

You stop crossing out when your cross-out number reaches
the SQUARE-ROOT of the highest number in your sieve.




Result:
-------

After doing this, your list should have all of its composite
numbers crossed out, and all of its prime numbers still intact.