121 (NUMBER)

'121' is the natural number following 120 and preceding 122.

Cardinal	One hundred [and] twenty-one
Ordinal	121st
Factorization	$11^2$
Roman numeral	CXXI
Binary	1111001
Hexadecimal	79

Contents

In mathematics

In other fields

References

In mathematics

'One hundred 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 ''x''³ - 4 (with ''x'' being 2 and 5, respectively).^[1]
It is also a star number and a centered octagonal number.
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. 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

'One hundred [and] twenty-one' is also:

★ The number for voicemail for mobile phones on the Vodafone network

★ The Lockheed EC-121 Warning Star

★ The year AD 121 or 121 BC.

★ The number of points required to win a standard game of cribbage.

★ The total number of days in the first four months of a leap year.

★ The number of cells on a Chinese checkers board.

★ The name of a song done by Powerline in ''A Goofy Movie''.

★ The Embraer EMB 121 Xingu, a Brazillian aircraft.

References

1. Wells, D. ''The Penguin Dictionary of Curious and Interesting Numbers'' London: Penguin Group. (1987): 136