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A Simple Algorithm for Prime Factorization and Primality Testing

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  • Kabenge Hamiss
  • Niansheng Tang

Abstract

We propose a new simple and faster algorithm to factor numbers based on the nature of the prime numbers contained in such composite numbers. It is well known that every composite number has a unique representation as a product of prime numbers. In this study, we focus mainly on composite numbers that contain a product of prime numbers that are greater than or equal to 5 which are of the form 6k+1 or 6k+5. Therefore, we use the condition that every prime or composite P of primes greater than or equal to 5 satisfies P2≡1 mod24. This algorithm is very fast especially when the difference in the prime components of a composite number (prime gap) is not so large. When the difference between the factors (prime gap) is not so large, it often requires just a single iteration to obtain the factors.

Suggested Citation

  • Kabenge Hamiss & Niansheng Tang, 2022. "A Simple Algorithm for Prime Factorization and Primality Testing," Journal of Mathematics, Hindawi, vol. 2022, pages 1-10, December.
    • Handle: RePEc:hin:jjmath:7034529
    DOI: 10.1155/2022/7034529
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