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.


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 repeated unit.