121 (number)

Template:More citations needed Template:Infobox number 121 (one hundred [and] twenty-one) is the natural number following 120 and preceding 122.

In mathematicsEdit

One hundred [and] twenty-one is

a square (11 times 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 <math>1 + p + p^2 + p^3 + p^4</math>, where p is prime (3, in this case).<ref>Template:Cite book</ref>
the sum of three consecutive prime numbers (37 + 41 + 43).
As <math>5! + 1 = 121</math>, it provides a solution to Brocard's problem. There are only two other squares known to be of the form <math>n! + 1</math>. 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 <math>x^{3}-4</math> (with Template:Mvar being 2 and 5, respectively).<ref>Wells, D., The Penguin Dictionary of Curious and Interesting Numbers, London: Penguin Group. (1987): 136</ref>
It is also a star number, a centered tetrahedral number, and a centered octagonal number.

A Chinese checkers board has 121 holes.

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 (<math>11^2</math>). But it cannot be expressed as the sum of any other number plus that number's digits, making 121 a self number.