Editing Repunit (section)

{{short description|Numbers that contain only the digit 1}}
{{pp-semi-indef|small=yes}}
{{Infobox integer sequence
| name = Repunit prime
| terms_number       = 11
| con_number         = Infinite
| first_terms        = [[11 (number)|11]], 1111111111111111111, 11111111111111111111111
| largest_known_term = (10<sup>8177207</sup>−1)/9
| OEIS               = A004022
| OEIS_name          = Primes of the form (10^n − 1)/9
}}

In [[recreational mathematics]], a '''repunit''' is a [[number]] like 11, 111, or 1111 that contains only the digit [[1 (number)|1]] &mdash; a more specific type of [[repdigit]]. The term stands for "repeated unit" and was coined in 1966 by Albert H. Beiler in his book ''Recreations in the Theory of Numbers''.{{refn|group=note|Albert H. Beiler coined the term "repunit number" as follows:<blockquote>A number which consists of a repeated of a single digit is sometimes called a monodigit number, and for convenience the author has used the term "repunit number" (repeated unit) to represent monodigit numbers consisting solely of the digit 1.<ref>{{Harvnb|Beiler|2013|pp=83}}</ref></blockquote>}}<!--- Original publication was 1964; did he coin repunit in that edition? or was this added in 1966? --->

A '''repunit prime''' is a repunit that is also a [[prime number]]. Primes that are repunits in [[Binary number|base-2]] are [[Mersenne prime]]s. As of October 2024, the [[largest known prime number]] {{nowrap|2<sup>136,279,841</sup> − 1}}, the largest [[probable prime]] ''R''<sub>8177207</sub> and the largest [[elliptic curve primality]]-proven prime ''R''<sub>86453</sub> are all repunits in various bases.