121 (number)

← 120 121 122 →
← 120 121 122 123 124 125 126 127 128 129 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred twenty-one
Ordinal	121st (one hundred twenty-first)
Factorization	112
Divisors	1, 11, 121
Greek numeral	ΡΚΑ´
Roman numeral	CXXI, cxxi
Binary	11110012
Ternary	111113
Senary	3216
Octal	1718
Duodecimal	A112
Hexadecimal	7916

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 ${\displaystyle 1+p+p^{2}+p^{3}+p^{4}}$, where p is prime (3, in this case). ^[1]
• the sum of three consecutive prime numbers (37 + 41 + 43).
• As ${\displaystyle 5!+1=121}$, it provides a solution to Brocard's problem. There are only two other squares known to be of the form ${\displaystyle n!+1}$. 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 ${\displaystyle x^{3}-4}$ (with x being 2 and 5, respectively). ^[2]
• It is also a star number, a centered tetrahedral number, and a centered octagonal number.

A Chinese checkers board has 121 holes.

• 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 (${\displaystyle 11^{2}}$). But it cannot be expressed as the sum of any other number plus that number's digits, making 121 a self number.

References

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