Repunit
A repunit (short for "repeated unit") is a number consisting only of the digit 1. More formally, a repunit is an integer of the form (10n - 1) / 9 for some positive integer n.
The term "repunit" was coined by Albert H. Beiler in his 1966 book, Recreations in the Theory of Numbers.
Repunits are often denoted as Rn, where n is the number of digits. Thus, R2 = 11, R5 = 11111, and so on.
The study of repunits often focuses on their prime factorization. Determining whether a repunit is prime can be computationally challenging due to their size. A repunit Rn can only be prime if n is itself prime. However, the converse is not true: if n is prime, Rn is not necessarily prime. Repunit primes are relatively rare.
Repunits have connections to other areas of number theory, including Mersenne primes and Fermat numbers. Their special structure makes them a subject of interest for mathematicians and computational number theorists.