121 (number)
From HandWiki
Short description: Natural number
| ||||
---|---|---|---|---|
Cardinal | one hundred twenty-one | |||
Ordinal | 121st (one hundred twenty-first) | |||
Factorization | 112 | |||
Divisors | 1, 11, 121 | |||
Greek numeral | ΡΚΑ´ | |||
Roman numeral | CXXI | |||
Binary | 11110012 | |||
Ternary | 111113 | |||
Quaternary | 13214 | |||
Quinary | 4415 | |||
Senary | 3216 | |||
Octal | 1718 | |||
Duodecimal | A112 | |||
Hexadecimal | 7916 | |||
Vigesimal | 6120 | |||
Base 36 | 3D36 |
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 [math]\displaystyle{ 1 + p + p^2 + p^3 + p^4 }[/math], where p is prime (3, in this case).[1]
- the sum of three consecutive prime numbers (37 + 41 + 43).
- As [math]\displaystyle{ 5! + 1 = 121 }[/math], it provides a solution to Brocard's problem. There are only two other squares known to be of the form [math]\displaystyle{ n! + 1 }[/math]. 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 [math]\displaystyle{ x^{3}-4 }[/math] (with x 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 ([math]\displaystyle{ 11^2 }[/math]). 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
- ↑ Ribenboim, Paulo (1994). Catalan's conjecture : are 8 and 9 the only consecutive powers?. Boston: Academic Press. ISBN 0-12-587170-8. OCLC 29671943.
- ↑ Wells, D., The Penguin Dictionary of Curious and Interesting Numbers, London: Penguin Group. (1987): 136
- ↑ Vodafone, Calling and messaging
- ↑ Rule 1.1 , American Cribbage Congress, retrieved 6 September 2011
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