On the last digits of consecutive primes
Abstract
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.
Keywords
Cite
@article{arxiv.1604.02443,
title = {On the last digits of consecutive primes},
author = {Fred B. Holt},
journal= {arXiv preprint arXiv:1604.02443},
year = {2016}
}
Comments
This third version of the manuscript increases the degree of the approximate model from 6 to 11, and we use Mertens' Third Theorem to extend the range over which we can give fair approximations for the relative populations of larger gaps