Identifying maximal-period large-order Multiple Recursive Generators (MRGs) necessitates advanced computational techniques. This chapter begins with an exploration of Algorithm AK, a well-established approach to searching for such generators. The discussion then shifts to the complexities involved in maximizing period lengths, including challenges in discovering suitable parameters. Algorithm GMP is introduced as a means of identifying generalized Mersenne primes, which play a pivotal role in constructing efficient MRGs. The chapter also examines critical computational steps, such as verifying primitive polynomials and analyzing prime factorization, culminating in a rigorous framework for the development of high-performance MRGs.