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Computational challenges and solutions: Prime number generation for enhanced data security.

Amal Ezz-Eldien1, Mohamed Ezz2, Amjad Alsirhani2

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This study introduces novel algorithms for efficient prime number generation, crucial for data security and computational tasks. These methods outperform existing algorithms in speed and flexibility for generating primes within specific ranges.

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Area of Science:

  • Computer Science
  • Number Theory
  • Cryptography

Background:

  • Efficient prime number generation is vital for data security, cryptography, and complex computations.
  • Existing algorithms face challenges in speed and flexibility for diverse applications.
  • The demand for secure communication necessitates improved prime number generation methods.

Purpose of the Study:

  • To present two novel algorithms for prime number generation.
  • To address the challenge of efficient prime number generation up to a limit and within a range.
  • To enhance performance and adaptability in prime number generation.

Main Methods:

  • Development of two new algorithms based on odd-composed number formulas.
  • Comparative analysis against established algorithms like Miller-Rabin and various Sieves.
  • Experimental evaluation of mean execution time and range-based generation performance.

Main Results:

  • Proposed algorithms demonstrate superior performance compared to Miller-Rabin, Sieve of Atkin, Sieve of Eratosthenes, and Sieve of Sundaram.
  • Algorithms achieve remarkable performance improvements in mean execution time.
  • Algorithms efficiently generate primes within specified ranges, outperforming existing methods.

Conclusions:

  • The novel algorithms offer significant performance enhancements for prime number generation.
  • The flexibility in generating primes by range impacts cryptographic systems and distributed computing.
  • These advancements support more secure communication, faster number theory computations, and broader research in computer science and mathematics.