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 (repeated 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:

(10ⁿ - 1) / 9

Repunits are a sub-set of repdigit numbers.

A Repunit prime is a repunit which is also prime.

Repdigit (repeated 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

External links

• Repunit