On Some Parallel Sieve of Prime Numbers Generation
On Some Parallel Sieve of Prime Numbers Generation
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UltracompuUr NoU #120 Page 2 Approximating i -th prime as i log i, and <})(n) as n/log n [ 1 ] we have CiN) ji^_N__ ^ ^ ^/^^ 1 1 = 2 (Z log/) 1 = 2 (j logo V^/IobVat 1 \ ^/log^ dx = A^loglogjT I 2 = A'loglog r v^_i llog'^J (xlogjr) - A'loglog2 = NloglogV]v - MogloglogVA^ - A^loglog2 = ~ ATloglogV^ = €KN loglogA^) The time complexity of the algorithm which is connected with saving memory, is: Where C(N) is the time complexity of Eratosthenes' algorithm and <^ f^A^ .
Thus, the time complexity of the algorithm for saving memory is the same as for classic Eratosthenes' siev'e - ©(A' loglog, V) .
5. Time Complexity of Parallel Algorithm From the very essence of the parallel algorithm it follows that for small number of pro- cessors P the work can be divided completely among the processors. Assuming that the speed of different processors is nearly the same it is easily seen that the additional work caused by checking divisibility by nonprimes takes place just at the first stage.
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To quickly assess the difficulty of the text, read a short excerpt:
UltracompuUr NoU #120 Page 2 Approximating i -th prime as i log i, and <})(n) as n/log n [ 1 ] we have CiN) ji^_N__ ^ ^ ^/^^ 1 1 = 2 (Z log/) 1 = 2 (j logo V^/IobVat 1 \ ^/log^ dx = A^loglogjT I 2 = A'loglog r v^_i llog'^J (xlogjr) - A'loglog2 = NloglogV]v - MogloglogVA^ - A^loglog2 = ~ ATloglogV^ = €KN loglogA^) The time complexity of the algorithm which is connected with saving memory, is: Where C(N) is the time complexity of Eratosthenes' algorithm and
What to read after On Some Parallel Sieve of Prime Numbers Generation?
You can find similar books in the "Read Also" column, or choose other free books by Vladimir Fleyshgakker to read online
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