121 (number)

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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
Senary	3216
Octal	1718
Duodecimal	A112
Hexadecimal	7916

Last updated October 08, 2024

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 $x$ 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 ( $11^{2}$ ). 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.

Related Research Articles

<span class="mw-page-title-main">Prime number</span> Number divisible only by 1 or itself

A prime number 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 of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.

A palindromic number is a number that remains the same when its digits are reversed. In other words, it has reflectional symmetry across a vertical axis. The term palindromic is derived from palindrome, which refers to a word whose spelling is unchanged when its letters are reversed. The first 30 palindromic numbers are:

19 (nineteen) is the natural number following 18 and preceding 20. It is a prime number.

In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals $32$ and can be written as $3 \times 3$ .

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 Recreations in the Theory of Numbers.

In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system. The word is a portmanteau of "repeated" and "digit". Examples are 11, 666, 4444, and 999999. All repdigits are palindromic numbers and are multiples of repunits. Other well-known repdigits include the repunit primes and in particular the Mersenne primes.

27 is the natural number following 26 and preceding 28.

A power of two is a number of the form $2 n$ where $n$ is an integer, that is, the result of exponentiation with number two as the base and integer $n$ as the exponent.

73 (seventy-three) is the natural number following 72 and preceding 74. In English, it is the smallest natural number with twelve letters in its spelled out name.

61 (sixty-one) is the natural number following 60 and preceding 62.

120 is the natural number following 119 and preceding 121. It is five sixths of a gross, or ten dozens.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

360 is the natural number following 359 and preceding 361.

<span class="mw-page-title-main">Cube (algebra)</span> Number raised to the third power

In arithmetic and algebra, the cube of a number $n$ is its third power, that is, the result of multiplying three instances of $n$ together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 2³ = 8 or $(x + 1) 3$ .

A powerful number is a positive integer m such that for every prime number p dividing m, p² also divides m. Equivalently, a powerful number is the product of a square and a cube, that is, a number m of the form m = a²b³, where a and b are positive integers. Powerful numbers are also known as squareful, square-full, or 2-full. Paul Erdős and George Szekeres studied such numbers and Solomon W. Golomb named such numbers powerful.

144 is the natural number following 143 and preceding 145.

In combinatorial mathematics, a large set of positive integers

At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime numbers. These problems were characterised in his speech as "unattackable at the present state of mathematics" and are now known as Landau's problems. They are as follows:

Goldbach's conjecture: Can every even integer greater than 2 be written as the sum of two primes?
Twin prime conjecture: Are there infinitely many primes p such that p + 2 is prime?
Legendre's conjecture: Does there always exist at least one prime between consecutive perfect squares?
Are there infinitely many primes p such that p − 1 is a perfect square? In other words: Are there infinitely many primes of the form n² + 1?

288 is the natural number following 287 and preceding 289. Because 288 = 2 · 12 · 12, it may also be called "two gross" or "two dozen dozen".

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 Archived 2015-01-18 at the Wayback Machine , American Cribbage Congress, retrieved 6 September 2011

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[1] Ribenboim, Paulo (1994). Catalan's conjecture : are 8 and 9 the only consecutive powers?. Boston: Academic Press. ISBN 0-12-587170-8. OCLC 29671943.

[2] Wells, D., The Penguin Dictionary of Curious and Interesting Numbers , London: Penguin Group. (1987): 136

[3] Vodafone, Calling and messaging

[4] Rule 1.1 Archived 2015-01-18 at the Wayback Machine , American Cribbage Congress, retrieved 6 September 2011

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121 (number)

Contents

In mathematics

In other fields

See also

Related Research Articles

References