Repunit

In mathematics, a repunit is a number like 11, 111, or 1111 that consists of repeated units, or 1's. A mathematical shorthand for a repunit is a capital "R" subscripted with the number of repeated units. 11 is therefore R₂, 111 R₃, and 1111 R₄. 11 is the first repunit and 111 the second, however, because although 1 is R₁, 1, for obvious reasons, is not a repunit.

Many reupunits are primes. For a repunit R_n to be prime, it is a necessary but not sufficient condition that the number (or sum) of its digits also be prime. For example, R₃, R₅, R₇ are not primes. Indexes for which repunits are primes are {2, 19, 23, 317, 1031, ...}. It is not known whether there are infinitely many prime repunits. Prime repunits are similar to a special class of primes that remain primes after any permutation of their digits. They are called permutable primes[?] or absolute primes[?].

See also:

• Repdigit.
• Table of Factors

Note: Some mathematical theoreticians regard the repunit as an arbitrary concept, arguing that it depends on the use of decimal numerals.

References

• Repunits at MathWorld: http://mathworld.wolfram.com/Repunit
• Factors of base-ten repunits at WorldOfNumbers: http://www.worldofnumbers.com/repunits.htm