Two excursions in digitally delicate primes

Abstract: In 1978, Murray Klamkin asked whether there are prime numbers such that if any digit in the prime is replaced by any other digit, the resulting number is composite. In 1979, several examples were published together with a proof by Paul Erdős that infinitely many such primes exist. Following the terminology of Jackson Hopper and Paul Pollack, we call such primes ``digitally delicate." The smallest digitally delicate prime is 294001. In this talk, we discuss some of the history surrounding digitally delicate primes, implications of prior work, and recent work by the speaker with Jeremiah Southwick and Jacob Juillerat.

number theory

Audience: researchers in the topic

Combinatorial and additive number theory (CANT 2021)

Series comments: This is the nineteenth in a series of annual workshops sponsored by the New York Number Theory Seminar on problems in combinatorial and additive number theory and related parts of mathematics.

Registration for the conference is free. Register at cant2021.eventbrite.com.

The conference website is www.theoryofnumbers.com/cant/ Lectures will be broadcast on Zoom. The Zoom login will be emailed daily to everyone who has registered on eventbrite. To join the meeting, you may need to download the free software from www.zoom.us.

The conference program, list of speakers, and abstracts are posted on the external website.