# On the origin of the prime numbers

God created the integers, all else is the work of man.-Leopold Kronecker

At the beginning of the early universe, before there was anything to be counted, before number theory, there was information theory. This point may be clarified by considering the following thought experiment.

If there were no prime numbers, \(\mathbb{N}\) would not exist and therefore \(\mathbb{Q}\) would not exist. But, we would still have:

\begin{equation} \Omega = \{0,1\} \end{equation}

so in the beginning we only had the Boolean operations.

Assuming a couple purely local rules for generating sequences \(\{0,1\}^*\) and assuming that information may be created but not destroyed, we might observe:

\begin{equation} 0 \rightarrow 1 \end{equation}

\begin{equation} 00 \rightarrow 01 \rightarrow 10 \rightarrow 11 \end{equation}

However, since \(\mathbb{N}\) is consistent with but not reducible to boolean algebra on \(\Omega\) and \(\mathbb{N}\) is required to define a theory of computation, the primes were probably part of the first act of creation as claimed by Kronecker.