# 121 (number)

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

 ← 120 121 122 →
Cardinalone hundred twenty-one
Ordinal121st
(one hundred twenty-first)
Factorization112
Divisors1, 11, 121
Greek numeralΡΚΑ´
Roman numeralCXXI
Binary11110012
Ternary111113
Senary3216
Octal1718
DuodecimalA112

## 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.

121 is also: