Study on Modified Sieve of Eratosthenes Using Discrete Fourier Transform
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Keywords:
Sieve of eratosthenes, Periodic sequence, Prime number, Discrete fourier transformAbstract
The Sieve of eratosthenes (SOE) is one of the simplest ways to obtain prime numbers on a smaller scale, by eliminating all the multiples of prime numbers up to a given value. The algorithm was slightly modified to eliminate the multiples of prime numbers, for all-natural numbers, rather than to a limit $n$. An algorithm was proposed using some basic properties of the sieve. Using the algorithm many arithmetic properties of the sequence obtained by modified SOE was discussed and generalized using Discrete fourier transform (DFT) and the results are helpful in strengthening the twin prime conjecture.
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