Random number generation is an essential step in cryptography, statistical analysis, and simulations. They are mostly used in Internet of Things (IoT), Cyclic Redundancy Checks (CRC), Advanced Encryption Standard (AES), etc. We offer a Pseudo-Random Number Generator (PRNG) in this article that makes use of several algorithms and methods to produce high-quality random numbers. A traditional 16-bit Linear Feedback Shift Register (LFSR) repeats its value after 65,535 clock cycles. In this article, we have endeavored to present a pioneering approach aimed at prolonging the cycle length of a LFSR as it confronts recurring values when harnessed in conjunction with the Fibonacci sequence generator. Our primary aim is to elevate the LFSR’s operational efficiency by substantially augmenting its cycle length. In pursuit of this objective, we have meticulously outlined an array of key insights and methodologies that collectively constitute a significant contribution to the field of digital sequence generation and cryptographic techniques. This study provides a thorough analysis and assessment of PRNGs, highlighting its design and performance. It is a useful for comprehending and choosing PRNGs that satisfy the needs of contemporary secure applications.