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111 is the third repunit number.

111 is the smallest Brazilian prime (nontrivial repunit prime, i.e. repunit prime with length ≥3) in base 10. (11 is trivial repunit prime in base 10, thus it is not Brazilian prime in base 10, but a Brazilian prime in base 3: 1110 = 1113)

111 is the largest known prime p such that (p^p+1)/(p+1) (the repunit number with length p in negative base −p) is (probable) prime. (the only other known such p are 3, 5, 15, note that these three primes are consecutive Fermat primes, but 111 is not Fermat prime)

All triplets in all bases are multiples of 111 in that base, therefore the number represented by 111 in a particular base is the only triplet that can ever be prime, 111 is prime in both base 10 and base 2 (1112 = 710), 111 is also prime in these bases up to 100: 2, 3, 5, 6, 8, 10, 12, 13, 15, 18, 19, 20, 23, 29, 32, 35, 42, 46, 49, 4E, 52, 56, 59, 5E, 63, 65, 66, 68, 75, 76, 83, 85, 89, 92, 93, 99, 9E, XE, E6, E9, EE

111 is the smallest irregular prime with irregular index > 1 (note that the prime index of 111 is exactly the smallest irregular prime (31))

The Mersenne number M111 (2^111−1) was once the smallest composite Mersenne number with prime exponent without any known prime factor.

111 is the largest repunit number such that itself is the largest number expression-able by using these many 1’s and {+, ×, ^} (for 1111 (4 1’s), the largest such number is 11^11)

111 is the smallest double-sexy prime, i.e. 111 and 111±6 are all primes, and no other primes between them.

111 is the smallest number n for which phi(2n + 1) is less than phi(2n), where phi is Euler totient function.

111 is the largest odd integer that cannot be expressed as the sum of four distinct nonzero squares with greatest common divisor 1.