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 ${\displaystyle 1+p+p^{2}+p^{3}+p^{4}}$, where p is prime (3, in this case).^[1]
• the sum of three consecutive prime numbers (37 + 41 + 43).
• As ${\displaystyle 5!+1=121}$, it provides a solution to Brocard's problem. There are only two other squares known to be of the form ${\displaystyle n!+1}$. 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 ${\displaystyle x^{3}-4}$ (with x being 2 and 5, respectively).^[2]
• 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 (${\displaystyle 11^{2}}$). 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^[3]
• The undiscovered chemical element unbiunium has the atomic number 121
• The official end score for cribbage^[4]
• The pennant number of RTS Moskva, the Russian Navy’s Black Sea flagship, which was damaged beyond repair on April 13, 2022.

See also

• List of highways numbered 121
• United States House of Representatives House Resolution 121
• United Nations Security Council Resolution 121

References