Repunit

Repunit prime
No. of known terms11
Conjectured no. of termsInfinite
First terms11, 1111111111111111111, 11111111111111111111111
Largest known term(108177207−1)/9
OEIS index
  • A004022
  • 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 — 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 October 2024, the largest known prime number 2136,279,841 − 1, the largest probable prime R8177207 and the largest elliptic curve primality-proven prime R86453 are all repunits in various bases.

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