While exploring Brocard’s Equation $n! + 1 = m^2$, which is known to have 3 solutions, st. $m,n \in \mathbf{N} $, we develop an algorithm to effectively store factorials of large numbers. First, we begin by prime-decomposing the factorial with the help of Legendre’s Formula. Then, we convert the resulting product of prime powers into a sum by taking logarithms of convenient base. Finally, we implement the algorithm to search for potential solutions in $ \mathbf{N} $ for Brocard’s Equation up to $100 \,000!$.