For example, he proved the infinitude of primes using the divergence of the harmonic series, and used analytic methods to gain some understanding of the way prime numbers are distributed.
Our world has grown smaller and seedier while the compass of the great unknown out there seems to expand even in its infinitude and grow ever more alien.
Moreover, an infinitude of other third-order univariate difference equations can be found by multiplying any of the three matrices together an arbitrary number of times in an arbitrary sequence.