121 (one hundred ndtwenty-one) is the

natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''cardinal ...

following

120 120 may refer to: *120 (number), the number * AD 120, a year in the 2nd century AD *120 BC, a year in the 2nd century BC *120 film, a film format for still photography * ''120'' (film), a 2008 film * 120 (MBTA bus) * 120 (New Jersey bus) * 120 (Ken ...

and preceding

122 122 may refer to: *122 (number), a natural number *AD 122, a year in the 2nd century AD *122 BC, a year in the 2nd century BC *122 (film), ''122'' (film), a 2019 Egyptian psychological horror film *"One Twenty Two", a 2022 single by the American roc ...

In mathematics

''One hundred ndtwenty-one'' is * a

square In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90- degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length a ...

(11 times 11) * the sum of the powers of 3 from 0 to 4, so a

repunit In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit. The term stands for repeated unit and was coined in 1966 by Albert H. Beiler in his book ''Recreat ...

in ternary. Furthermore, 121 is the only square of the form

1 + p + p^2 + p^3 + p^4

, where ''p'' is prime (3, in this case). * the sum of three consecutive

prime number A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

s (37 + 41 + 43). * As

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

. 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^-4

(with being 2 and 5, respectively). * It is also a

star number A star number is a centered figurate number, a centered hexagram (six-pointed star), such as the Star of David, or the board Chinese checkers is played on. The ''n''th star number is given by the formula ''Sn'' = 6''n''(''n'' − 1) + 1. The ...

, a centered tetrahedral number, and a

centered octagonal number A centered octagonal number is a centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers.. The centered octagonal numbers are the same as the od ...

* In decimal, it is a

Smith number In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its prime factorization in the given number base. In the case of numbers that are not square-f ...

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 A Friedman number is an integer, which represented in a given numeral system, is the result of a non-trivial expression using all its own digits in combination with any of the four basic arithmetic operators (+, −, ×, ÷), additive inverses, pa ...

(

11^2

). But it cannot be expressed as the sum of any other number plus that number's digits, making 121 a

self number In number theory, a self number or Devlali number in a given number base b is a natural number that cannot be written as the sum of any other natural number n and the individual digits of n. 20 is a self number (in base 10), because no such combina ...

In other fields

121 is also: * The

electricity Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as describ ...

emergency telephone number Most public switched telephone networks have a single emergency telephone number (sometimes known as the universal emergency telephone number or the emergency services number) that allows a caller to contact local emergency services for assis ...

Egypt Egypt ( ar, مصر , ), officially the Arab Republic of Egypt, is a transcontinental country spanning the northeast corner of Africa and southwest corner of Asia via a land bridge formed by the Sinai Peninsula. It is bordered by the Medit ...

* The number for

voicemail A voicemail system (also known as voice message or voice bank) is a computer-based system that allows users and subscribers to exchange personal voice messages; to select and deliver voice information; and to process transactions relating to ind ...

for

mobile phone A mobile phone, cellular phone, cell phone, cellphone, handphone, hand phone or pocket phone, sometimes shortened to simply mobile, cell, or just phone, is a portable telephone that can make and receive calls over a radio frequency link whi ...

s on the

Vodafone Vodafone Group plc () is a British multinational telecommunications company. Its registered office and global headquarters are in Newbury, Berkshire, England. It predominantly operates services in Asia, Africa, Europe, and Oceania. , Vod ...

network * The undiscovered

chemical element A chemical element is a species of atoms that have a given number of protons in their nuclei, including the pure substance consisting only of that species. Unlike chemical compounds, chemical elements cannot be broken down into simpler sub ...

unbiunium Unbiunium, also known as eka-actinium or simply element 121, is the hypothetical chemical element with symbol Ubu and atomic number 121. ''Unbiunium'' and ''Ubu'' are the temporary systematic IUPAC name and symbol respectively, which are used unt ...

has the atomic number 121 * The official end score for

cribbage Cribbage, or crib, is a card game, traditionally for two players, that involves playing and grouping cards in combinations which gain points. It can be adapted for three or four players. Cribbage has several distinctive features: the cribbag ...

Rule 1.1
, American Cribbage Congress, retrieved 6 September 2011 * The pennant number of RTS Moskva, the Russian Navy’s Black Sea flagship, which was damaged beyond repair on April 13, 2022.

References

{{DEFAULTSORT:121 (Number) Integers

In mathematics

In other fields

See also

References