@MISC{Shallit01minimalprimes, author = {Jeffrey Shallit}, title = {Minimal Primes}, year = {2001} }

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Abstract

Introduction Recreations involving the decimal digits of primes have a long history. To give just a few examples, without trying to be exhaustive, Yates [8] studied the \repunits", which are primes with base-10 representation of the form 111 1. Caldwell and Dubner [3] studied the \nearrepunits ", which are primes of n decimal digits containing n 1 ones and 1 zero. Card [4] introduced prime numbers such as 37337999, in which every nonempty pre x is also a prime; he called them \snowball" primes. These were later studied by Angell & Godwin [1] and Caldwell [2], who called them \right-truncatable" primes. They also studied the \left-truncatable" primes, such as 4632647, in which every nonempty sux is prime. Kahan and Weintraub [6] gave a list of all the left-truncatable primes. Huestis [5] introduced the \recursively laminar primes". In this note, I discuss an apparently new problem on the decimal digits of primes | but one inspired from a classical theorem in formal language the