  We report preliminary results on using the MEMCPU\texttrademark{} Platform to
compute the prime factorization of large biprimes. The first approach, the
direct model, directly returns the factors of a given biprime. The second
approach, the congruence model, returns smooth congruences to address the
bottleneck of standard sieve methods. The models have size-dependent structure,
and the MEMCPU Platform requires structure-dependent tuning for optimal
performance. Therefore, for both models, we tuned the platform on sample
problems up to a given size according to available resources. Then we generated
RSA-like benchmark biprimes to perform rigorous scaling analysis. The MEMCPU
timings over the tuned range followed low degree polynomials in the number of
bits, markedly different than other tested methods including general number
field sieve. MEMCPU's congruence model was the most promising, which was scaled
up to 300-bit factorization problems while following a $2^{nd}$ degree
polynomial fit. We also discuss the approach to tuning the MEMCPU Platform for
problems beyond the reach of today's most advanced methods. Finally, basic
analysis of the acceleration expected from an ASIC implementation is provided
and suggests the possibility of real time factorization of large biprimes.

Emerging Technologies;Cryptography and Security;Adaptation and Self-Organizing Systems