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Efficient Pseudo Random Number Generator (PRNG) Design on FPGA | Random Number Generators (RNGs) are substantially used in many security domains, providing a fundamental source of unpredictability essential for tasks such as cryptography, simulations, and statistical analyses. The efficiency and quality of an RNG directly impact the reliability and security of diverse applications, making advancements in RNG design, as explored in this study, of significant importance for enhancing computational processes. This paper presents an innovative Pseudo-Random Number Generator (PRNG) that leverages the efficiency of two carefully selected Linear Feedback Shift Registers (LFSRs) and a connecting XOR gate. The investigation of five polynomials identified an optimal pair, resulting in a notable improvement of over 200X in the length of random bit sequences compared to a single LFSR-based PRNG. The Basys3 FPGA board with the xc7a35tcpg236-1 FPGA chip was used to implement and synthesize the proposed design. Two significant findings emerge from this research. Firstly, using variable polynomials demonstrates a huge enhancement in the duration of randomness, outperforming the impact of variable seeds. A noteworthy observation is that employing the same polynomials in different branches does not result in optimal results. Secondly, managing more seeds is associated with an increased area cost, underscoring the efficiency of handling two polynomials.