121 (one hundred [and] twenty-one) is the natural number following 120 and preceding 122.
In mathematics
121 is a square (11 × 11) the sum of the powers of 3 from 0 to 4, so a repunit in ternary. Furthermore, 121 is the only square of the form , where p is prime (3, in this case). the sum of three consecutive prime numbers (37 + 41 + 43). As , it provides a solution to Brocard's problem. There are only two other squares known to be of the form . Another example of 121 being one of the few numbers supporting a conjecture is that Fermat conjectured that 4 and 121 are the only perfect squares of the form (with being 2 and 5, respectively).Wells, D., The Penguin Dictionary of Curious and Interesting Numbers, London: Penguin Group. (1987): 136 It is also a star number, a centered tetrahedral number, and a centered octagonal number.
In decimal, it is a Smith number since its digits add up to the same value as its factorization (which uses the same digits) and as a consequence of that it is a Friedman number (). But it cannot be expressed as the sum of any other number plus that number's digits, making 121 a self number. The smallest composite number to not be a multiple of 2, 3, 5 or 7.
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