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Abstract: Generation of prime numbers and factorization are very important topics in number theory and cryptography. Sieve-based methods like Sieve of Eratosthenes and Sieve of Euler have widespread usage. Pollard’s Rho algorithm, a probabilistic method for integer factorization, is also widely used in cryptographic applications. This paper explores a parallel approach alternative to these methods employing CPU and GPU acceleration to improve efficiency. Although parallelization imposes overhead on small inputs, experience suggests significant speedup for bigger prime boundaries. Our experiments show the potential of parallel computation to improve cryptographic computations, and in particular, this paper aims to demonstrate how increasing the number of CPUs in a system impacts the performance of these algorithms.