In mathematics, a **repunit** (from the words *repeated* and *unit*) is a number like 11, 111, or 1111 that consists of **rep**eated **unit**s, or 1's. A mathematical shorthand for a repunit is a capital "R" subscripted with the number of repeated units. 11 is therefore R_{2}, 111 R_{3}, and 1111 R_{4}. 11 is the __first__ repunit and 111 the second, however, because although 1 is R_{1}, 1, for obvious reasons, is not a repunit.

A **repunit prime** is simply a repunit that is a prime number. For a repunit R_{n} to be prime, it is a necessary but not sufficient condition that the number (or sum) of its digits also be prime. For example, R_{3}, R_{5}, R_{7} are not primes. Indexes for which repunits are primes are {2, 19, 23, 317, 1031, ...}. It is not known whether there are infinitely many prime repunits. Prime repunits are similar to a special class of primes that remain primes after any permutation of their digits. They are called permutable primes or absolute primes.

In binary, all repunit primes are also Mersenne primes.

**See also**:

**References**

- Repunits at MathWorld: http://mathworld.wolfram.com/Repunit.html
- Factors of base-ten repunits at WorldOfNumbers: http://www.worldofnumbers.com/repunits.htm
- Paulo Ribenboim,
*The Book Of Prime Number Records*.