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Prime Number Sieve

Next_Prime = 3 ====> Mark multiples of 3 as non-prime. 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 . Prime Number Sieve.

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Prime Number Sieve

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  1. Next_Prime = 3 ====> Mark multiples of 3 as non-prime. 23 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 Prime Number Sieve Next_Prime = 2 ====> Mark multiples of 2 as non-prime. 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

  2. Next_Prime = 5 ====> Mark multiples of 5 as non-prime. Next_Prime = 7 ====> Mark multiples of 7 as non-prime. 23 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 23 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 Prime Number Sieve (cont’d) Optimization #1 Q:Do you need to mark multiples of 11 between 1 and 50 ? A: No ! (They are already marked by the help of primes ≤ 7) Optimization #2 Q:Do you need to mark multiples of 7 between 1 and 48? A: No ! (They are already marked by the help of primes < 7)

  3. Sequential Time Complexity Analysis Optimization #1: Optimization #2:

  4. Parallel Time Complexity Analysis Another Formulation:

  5. Programming Project: Parallel Prime Number Generation Read at: http://www.mst.edu/~ercal/387/387.html

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