121 (number)

| ← 120 121 122 → | | | | --- | --- | --- | | ← 120 | 121 | 122 → | | ← 120 121 122 123 124 125 126 127 128 129 → .mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:"\a0 · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}List of numbersIntegers← 0 100 200 300 400 500 600 700 800 900 → | | | | one hundred twenty-one | | | | 121st(one hundred twenty-first) | | | | 112 | | | | 1, 11, 121 | | | | ΡΚΑ´ | | | | .mw-parser-output .roman-numeral{font-family:"Nimbus Roman No9 L","Times New Roman",Times,serif;font-size:118%;line-height:1}.mw-parser-output .roman-numeral-a{border:1px solid}.mw-parser-output .roman-numeral-t{border-top:1px solid}.mw-parser-output .roman-numeral-v{border:solid;border-width:0 1px;padding:0 2px}.mw-parser-output .roman-numeral-h{border:solid;border-width:1px 0}.mw-parser-output .roman-numeral-tv{border:1px solid;border-bottom:none;padding:0 2px}CXXI, cxxi | | | | 11110012 | | | | 111113 | | | | 3216 | | | | 1718 | | | | A112 | | | | 7916 | | |

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

121 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
  

  {\displaystyle 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
  

  {\displaystyle 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
  

{\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

      x
      
        3
      
    
    −
    4
  

{\displaystyle 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.

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 (

      11
      
        2
  

  {\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.