121 (number)

Short description: Natural number

← 120 121 122 →
← 120 121 122 123 124 125 126 127 128 129 → List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred twenty-one
Ordinal	121st (one hundred twenty-first)
Factorization	112
Divisors	1, 11, 121
Greek numeral	ΡΚΑ´
Roman numeral	CXXI
Binary	11110012
Ternary	111113
Quaternary	13214
Quinary	4415
Senary	3216
Octal	1718
Duodecimal	A112
Hexadecimal	7916
Vigesimal	6120
Base 36	3D36

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 [math]\displaystyle{ 1 + p + p^2 + p^3 + p^4 }[/math], where p is prime (3, in this case).
• the sum of three consecutive prime numbers (37 + 41 + 43).
• As [math]\displaystyle{ 5! + 1 = 121 }[/math], it provides a solution to Brocard's problem. There are only two other squares known to be of the form [math]\displaystyle{ n! + 1 }[/math]. 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 [math]\displaystyle{ x^{3}-4 }[/math] (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 ([math]\displaystyle{ 11^2 }[/math]). 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
• The undiscovered chemical element unbiunium has the atomic number 121
• The official end score for cribbage
• 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