Finding a Widely Digitally Delicate Prime
Jon Grantham
TL;DR
This paper delivers the first explicit example of a widely digitally delicate prime by leveraging a modified covering-system construction. It builds on Filaseta and Southwick's result by producing a congruence class with guaranteed composite variations after digit changes, aided by explicit factors of Phi_n(10) to replace unknown primes. The authors implement a PARI/GP CRT assembly and a PARI/C pipeline to search candidates and verify the digit-variation property, culminating in a 4032-digit prime with a formal primality certificate (ECPP). This work demonstrates a feasible pathway to explicit constructions of digit-dependent primes and has implications for the study of covering systems and repunit factorization in primality problems.
Abstract
This paper describes the construction of the first explicitly known widely digitally delicate prime.