121 (number) explained

Number:	121
Divisor:	1, 11, 121

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

1 + p + p ^{2} + p ^{3} + p ^{4} , where p is prime (3, in this case).^[1]

• the sum of three consecutive prime numbers (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 ^{3} -4 (with being 2 and 5, respectively).^[2]

• It is also a star number, a centered tetrahedral number, and a centered octagonal number.

• 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 (

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 other fields

121 is also:

• The electricity emergency telephone number in Egypt
• The number for voicemail for mobile phones on the Vodafone network^[3]
• The undiscovered chemical element unbiunium has the atomic number 121
• The official end score for cribbage^[4]
• 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

References

1. Book: Ribenboim, Paulo . Catalan's conjecture : are 8 and 9 the only consecutive powers? . Academic Press . Boston . 1994 . 0-12-587170-8 . 29671943.
2. Wells, D., The Penguin Dictionary of Curious and Interesting Numbers, London: Penguin Group. (1987): 136
3. Vodafone, Calling and messaging
4. http://www.cribbage.org/rules/rule1.asp#section1 Rule 1.1