repunit
Sign in to saveIn recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — 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.
Key facts
- Integer sequence.name
- Repunit prime
- Integer sequence.terms_number
- 11
- Integer sequence.con_number
- Infinite
- Integer sequence.first_terms
- 11, 1111111111111111111, 11111111111111111111111
- Integer sequence.largest_known_term
- (108177207−1)/9
- Integer sequence.OEIS
- A004022
- Integer sequence.OEIS_name
- Primes of the form (10^n − 1)/9
via Wikipedia infobox
~15 min read
Article
15 sectionsContents
- Definition
- Properties
- Factorization of decimal repunits
- Repunit primes
- <span class="anchor" id="Decimal repunit primes"></span>Decimal repunit primes
- Algebra factorization of generalized repunit numbers
- The generalized repunit conjecture
- History
- Demlo numbers
- See also
- Footnotes
- Notes
- References
- References
- External links
In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — 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.
A repunit prime is a repunit that is also a prime number. Primes that are repunits in base-2 are Mersenne primes. As of May 2025, the largest known prime number , the largest probable prime R8177207 and the largest elliptic curve primality-proven prime R109297 are all repunits in various bases.