# Definition:Repunit Prime

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## 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.

When $b$ is the usual base $10$, such a prime is merely referred to as a **repunit 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**.

Some sources use the term **isoprime**.

## Linguistic Note

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

## Sources

- 2005: Clifford A. Pickover:
*A Passion for Mathematics*: Cool Numbers: The grand search for isoprimes