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Wiktionary
repunit

n. A number consisting entirely of the digit 1.

Wikipedia
Repunit

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.