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
Octal1718
DuodecimalA112
Hexadecimal7916

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 base 3. Furthermore 121 is the only square of the form  , where p is prime (3, in this case).[citation needed]
  • the sum of three consecutive primes (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 x3 - 4 (with x being 2 and 5, respectively).[1]
  • It is also a star number and a centered octagonal number.
 
A Chinese checkers board has 121 holes
  • In base 10, 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 can not 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

ReferencesEdit

  1. ^ Wells, D., The Penguin Dictionary of Curious and Interesting Numbers, London: Penguin Group. (1987): 136
  2. ^ Vodafone, Calling and messaging
  3. ^ Rule 1.1 Archived 2015-01-18 at the Wayback Machine, American Cribbage Congress, retrieved 6 September 2011