Study on Modified Sieve of Eratosthenes Using Discrete Fourier Transform

# S. R. Muthubharathi^{1}

^{1}78/1, Bharathi Nagar, Paundamangalam, Paramathi Velur, Namakkal, Tamil Nadu, India.**Abstract:** 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.

**Keywords:** Sieve of eratosthenes, Periodic sequence, Prime number, Discrete fourier transform.

**Cite this article as:** S. R. Muthubharathi, *Study on Modified Sieve of Eratosthenes Using Discrete Fourier Transform*, Int. J. Math. And Appl., vol. 10, no. 1, 2022, pp. 17-25.

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