Selecting efficient algorithm for generating prime numbers is necessary for various purposes
such as encryption, cryptography, generating complex passwords, system verification and …

We make two algorithms that generate all prime numbers up to a given limit, they are a
development of sieve of Eratosthenes algorithm, we use two formulas to achieve this …

This paper addresses the computational methods and challenges associated with prime
number generation, a critical component in encryption algorithms for ensuring data security …

Primes are the most mysterious figures amongst the positive integers. The fact that their
sequence hitherto lacks a known simplistic formula generating successive primes poses a …

This paper presents a new method for generating all prime numbers up to a particular
number m∈ N, m⩾ 9, by using the set theory. The proposed method is explicit and works …

Prime numbers are unique numbers. Prime numbers are numbers that only have a dividing
factor consisting of numbers 1 and the number itself. The prime numbers from 1 to n that are …

Prime numbers are widely used in many fields from engineering to medicine, especially
cryptology. The security of cryptographic systems is based on difficult mathematical …

Public-key cryptosystems base their security on well-known number-theoretic problems,
such as factorisation of a given number n. Hence, prime number generation is an absolute …

Genetic algorithms are well-known and frequently used heuristic methods for solving
optimization problems. In modern cryptography the generation of large primes has an …

In the process of devising better and better sieves for generation of prime numbers, the
efforts gradually lead to the classical Sieve of Eratosthenes. The main theme of Sieve of …