Why Mersenne Primes Are So Special?

Abstract

Mersenne primes and their Gaussian variants play a key role in TGD-based model of hadrons and elementary particles. In this article, quantum information theoretic arguments for the special role of Mersenne primes are discussed. The main idea is that information storage as states of prime-dimension state space is stable against self-reductions of state since these spaces cannot be decomposed to a tensor product so that the notion of entanglement does not even make sense. Mersenne primes M_k=2^k-1 are nearest to a power of two. Quantum computation would take place in 2^k-dimensional state space of k qubits and storage in 2^k-1 dimensional state space to which outcome of computation would be mapped isometrically.