On a conjecture regarding primality of numbers constructed from prepending and appending identical digits

TL;DR

This paper disproves a conjecture suggesting that adding identical digits to both ends of a number yields a non-prime only if the number is an even-digit palindrome, by providing counterexamples including 231 and 420.

Contribution

It demonstrates that the conjecture is false by identifying specific counterexamples and infinitely many such cases, expanding understanding of number construction and primality.

Findings

Counterexamples to the conjecture include n=231 and n=420.

The property holds for infinitely many values of n.

The original conjecture is therefore false.

Abstract

Consider the operation of adding the same number of identical digits to the left and to the right of a number n. In OEIS sequence A090287, it was conjectured that this operation will not produce a prime if and only if n is a palindrome with an even number of digits. We show that this conjecture is false by showing that this property also holds for n=231, n=420, and an infinite number of other values of n.