  Recently Oliver and Soundararajan made conjectures based on computational
enumerations about the frequency of occurrence of pairs of last digits for
consecutive primes. By studying Eratosthenes sieve, we have identified discrete
dynamic systems that exactly model the populations of gaps across stages of
Eratosthenes sieve. Our models provide some insight into the observed biases in
the occurrences of last digits in consecutive primes, and the models suggest
that the biases will ultimately be reversed for large enough primes.
  The exact model for populations of gaps across stages of Eratosthenes sieve
provides a constructive complement to the probabilistic models rooted in the
work of Hardy and Littlewood, and it provides time constants that describe the
evolution of the populations of larger gaps.
