121 (number)

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

← 120 122 → 121
← 120 121 122 123 124 125 126 127 128 129 → List of numbers — Integers ← 100 110 120 130 140 150 160 170 180 190 →
Cardinal	one hundred [and] twenty-one
Ordinal	121st (one hundred [and] twenty-first)
Numeral system	121
Factorization	$11^2$
Divisors	1, 11, 121
Roman numeral	CXXI
Binary	11110012
Octal	1718
Duodecimal	A112
Hexadecimal	7916

In mathematics

One hundred [and] twenty-one is a square and is the sum of three consecutive primes (37 + 41 + 43). There are no squares besides 121 known to be of the form $1 + p + p^2 + p^3 + p^4$, where p is prime (3, in this case). Other such squares must have at least 35 digits.

There are only two other squares known to be of the form n! + 1, supporting Brocard's conjecture. Another example of 121 being of the few examples 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).

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 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

See also

• List of highways numbered 121
• United States House of Representatives House Resolution 121
• United Nations Security Council Resolution 121