121 (number)

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

← 120
122 →
121
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

Contents

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 %2B p %2B p^2 %2B p^3 %2B 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).[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 (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:

See also

References

  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, American Cribbage Congress, retrieved 6 September 2011