Definition:Repunit Prime

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 repeated unit.

Sources

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