Lady_Aleena, the Sieve of Eratosthenes is a well-known approach to generating primes. To illustrate, suppose you want to generate the primes between 2 and 20 (as neither 0 and 1 are prime, by definition).

  1. Write out the list of numbers from 2 to 20 (this johngg does by creating a vector, with the bits for 0 and 1 set to 1):
    As numbers: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
    As vector: 110000000000000000000
Position:  000000000011111111112
           012345678901234567890
  2. For each number not marked off the list, mark off its multiples (johngg does this by setting that bit of the vector to '1'):
    1. For 2: 
      As numbers: 0 1  2 3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20 
      As vector: 110010101010101010101
Position:  000000000011111111112
           012345678901234567890
    2. For 3: 
      As numbers: 0 1 2 3  4  5  6  7  8 9 10  11  12  13  14 15 16  17  18  19  20 
      As vector: 110010101110101110101
Position:  000000000011111111112
           012345678901234567890

    Because the square root of 20 is approximately 4.5, we don't have to try the exercise with values beyond 5; thus our list of primes would be: 

    2 3 5 7 11 13 17 19
    As vector: 110010101110101110101
Position:  000000000011111111112
           012345678901234567890
    The vector bits at 2, 3, 5, 7, 11, 13, 17, and 19 are not set (0), indicating those values are prime.

Hope that helps.

Update: 2015-04-01
Updated formatting of example lines to highlight overstrike of values.

In reply to Re^5: Number functions I have lying around by atcroft
in thread Number functions I have lying around by Lady_Aleena

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