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# 121 (number)

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 Title: 121 (number) Author: World Heritage Encyclopedia Language: English Subject: Collection: Integers Publisher: World Heritage Encyclopedia Publication Date:

### 121 (number)

 ← 120 121 122 →
Cardinal one hundred twenty-one
Ordinal 121st
(one hundred and twenty-first)
Factorization 112
Divisors 1, 11, 121
Roman numeral CXXI
Binary 11110012
Ternary 111113
Quaternary 13214
Quinary 4415
Senary 3216
Octal 1718
Duodecimal A112
Vigesimal 6120
Base 36 3D36

121 (one hundred [and] twenty-one) is the natural number following 120 and preceding 122.

## Contents

• In mathematics 1
• In other fields 2
• References 4

## In mathematics

One hundred [and] twenty-one is a square and is the sum of three consecutive primes (37 + 41 + 43). There are no squares besides 121 known to be of the form 1 + p + p^2 + p^3 + p^4, where p is prime (3, in this case). Other such squares must have at least 35 digits.

There are only two other squares known to be of the form n! + 1, supporting Brocard's conjecture. Another example of 121 being of the few examples supporting a conjecture is that Fermat conjectured that 4 and 121 are the only perfect squares of the form x3 - 4 (with x being 2 and 5, respectively).

It is also a star number and a centered octagonal number.

In base 10, 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 can not be expressed as the sum of any other number plus that number's digits, making 121 a self number.

121 is also: