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# 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.

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

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 |