Английская Википедия:121 (number)
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Шаблон:Infobox number 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>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>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>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>x^{3}-4</math> (with Шаблон:Mvar 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>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
- ↑ Шаблон:Cite book
- ↑ Wells, D., The Penguin Dictionary of Curious and Interesting Numbers, London: Penguin Group. (1987): 136
- ↑ Vodafone, Calling and messaging
- ↑ Rule 1.1 Шаблон:Webarchive, American Cribbage Congress, retrieved 6 September 2011
