121 (number)

121 (one hundred [and] twenty-one) is the natural number following 120 and preceding 122.

In mathematics
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 $$1 + p + p^2 + p^3 + p^4$$, where p is prime (3, in this case).
 * the sum of three consecutive prime numbers (37 + 41 + 43).
 * As $$5! + 1 = 121$$, it provides a solution to Brocard's problem. There are only two other squares known to be of the form $$n! + 1$$. 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 $$x^{3}-4$$ (with $x$ being 2 and 5, respectively).
 * 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 ($$11^2$$). But it cannot be expressed as the sum of any other number plus that number's digits, making 121 a self number.

In other fields
121 is also:
 * The electricity emergency telephone number in Egypt
 * The number for voicemail for mobile phones on the Vodafone network
 * The undiscovered chemical element unbiunium has the atomic number 121
 * The official end score for cribbage
 * The pennant number of RTS Moskva, the Russian Navy’s Black Sea flagship, which was damaged beyond repair on April 13, 2022.