# Definition:Repunit Prime

Jump to navigation
Jump to search

## Definition

Let $b \in \Z_{>1}$ be an integer greater than $1$.

A **repunit prime base $b$** is a repunit base $b$ which is prime.

### Index

The **index** of a **repunit prime** is the number of digits it has.

Thus $R_n$ denotes a **repunit prime** with $n$ digits.

## Sequence

The sequence of repunit primes (base $10$) begins:

- $11, 1 \, 111 \, 111 \, 111 \, 111 \, 111 \, 111, 11 \, 111 \, 111 \, 111 \, 111 \, 111 \, 111 \, 111, \ldots$

## Also known as

Some sources are inevitably going to refer to a **repunit prime** as a **prime repunit**.

## Linguistic Note

The derivation of the term **repunit** is clear: it comes from **rep**eated **unit**.