121 (number)

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

← 120 121 122 →
Cardinalone hundred twenty-one
(one hundred twenty-first)
Divisors1, 11, 121
Greek numeralΡΚΑ´
Roman numeralCXXI

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  , where p is prime (3, in this case).[1]
  • 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 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 ( ). But it cannot be expressed as the sum of any other number plus that number's digits, making 121 a self number.

In other fieldsEdit

121 is also:

See alsoEdit


  1. ^ Ribenboim, Paulo (1994). Catalan's conjecture : are 8 and 9 the only consecutive powers?. Boston: Academic Press. ISBN 0-12-587170-8. OCLC 29671943.
  2. ^ Wells, D., The Penguin Dictionary of Curious and Interesting Numbers, London: Penguin Group. (1987): 136
  3. ^ Vodafone, Calling and messaging
  4. ^ Rule 1.1 Archived 2015-01-18 at the Wayback Machine, American Cribbage Congress, retrieved 6 September 2011