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

This paper addresses the computational methods and challenges associated with prime
number generation, a critical component in encryption algorithms for ensuring data security.
The generation of prime numbers efficiently is a critical challenge in various domains, including
cryptography, number theory, and computer science. The quest to find more effective
algorithms for prime number generation is driven by the increasing demand for secure communication
and data storage and the need for efficient algorithms to solve complex mathematical
problems. Our goal is to address this challenge by presenting two novel algorithms
for generating prime numbers: one that generates primes up to a given limit and another
that generates primes within a specified range. These innovative algorithms are founded on
the formulas of odd-composed numbers, allowing them to achieve remarkable performance
improvements compared to existing prime number generation algorithms. Our comprehensive
experimental results reveal that our proposed algorithms outperform well-established
prime number generation algorithms such as Miller-Rabin, Sieve of Atkin, Sieve of Eratosthenes,
and Sieve of Sundaram regarding mean execution time. More notably, our algorithms
exhibit the unique ability to provide prime numbers from range to range with a
commendable performance. This substantial enhancement in performance and adaptability
can significantly impact the effectiveness of various applications that depend on prime numbers,
from cryptographic systems to distributed computing. By providing an efficient and
flexible method for generating prime numbers, our proposed algorithms can develop more
secure and reliable communication systems, enable faster computations in number theory,
and support advanced computer science and mathematics research.