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Prime Number Sieve 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 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 Next_Prime = 3 ====> Mark multiples of 3 as non-prime.

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Prime Number Sieve (cont’d) 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 Next_Prime = 5 ====> Mark multiples of 5 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 Next_Prime = 7 ====> Mark multiples of 7 as non-prime. 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)

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

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Parallel Time Complexity Analysis Another Formulation:

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

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An ancient method for finding the prime numbers. Eratosthenes was a Greek mathematician from Cyrene (modern day Libya!). He was born in 276 BC, and.

An ancient method for finding the prime numbers. Eratosthenes was a Greek mathematician from Cyrene (modern day Libya!). He was born in 276 BC, and.

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