Currently there may be errors shown on top of a page, because of a missing Wiki update (PHP version and extension DPL3). |

**Navigation**

Topics | Help • Register • News • History • How to • Sequences statistics • Template prototypes |

# Repunit

A **repunit** is a number in any base that is made of only of 1's for each digit. All Mersenne numbers are repunit (**rep**eated **unit**, "1" being the number referred to as "unity") numbers. 111 is a repunit, in base 2 it is equal to 7 (base 10), in base 3 it is equal to 13 (base 10).

Repunit numbers are of the form:

- (10
^{n}- 1) / 9

Repunits are a sub-set of repdigit numbers.

A **Repunit prime** is a repunit which is also prime.

Repdigit (**rep**eated **digit**) numbers are sub-set of palindromic numbers.

A **Generalized repunit** for any base `b` ≥ 2 is defined as

- [math]\displaystyle{ (b^n-1)\over (b-1) }[/math].

So, Mersenne primes are a small sub-set of numbers that fits within the larger classes. The following table shows how these are related (with each group getting smaller on each succesive line.)

Palindromic |

[math]\displaystyle{ \Downarrow }[/math] |

Repdigit (Palidromes using a single digit) |

[math]\displaystyle{ \Downarrow }[/math] |

Repunit(Repdigit, digit = 1) |

[math]\displaystyle{ \Downarrow }[/math] |

Mersenne number (Base 2 repunit) |

[math]\displaystyle{ \Downarrow }[/math] |

Mersenne prime |