English

Digitally delicate primes

Number Theory 2015-10-14 v2

Abstract

Tao has shown that in any fixed base, a positive proportion of prime numbers cannot have any digit changed and remain prime. In other words, most primes are "digitally delicate". We strengthen this result in a manner suggested by Tao: A positive proportion of primes become composite under any change of a single digit and any insertion a fixed number of arbitrary digits at the beginning or end.

Keywords

Cite

@article{arxiv.1510.03401,
  title  = {Digitally delicate primes},
  author = {Jackson Hopper and Paul Pollack},
  journal= {arXiv preprint arXiv:1510.03401},
  year   = {2015}
}

Comments

8+epsilon pages; minor corrections made, additional references added

R2 v1 2026-06-22T11:18:26.350Z