# 109 (number)

Short description: Natural number
 ← 108 109 110 →
Cardinalone hundred nine
Ordinal109th
(one hundred ninth)
Factorizationprime
Prime29th
Divisors1, 109
Greek numeralΡΘ´
Roman numeralCIX
Binary11011012
Ternary110013
Quaternary12314
Quinary4145
Senary3016
Octal1558
Duodecimal9112
Vigesimal5920
Base 363136

109 (one hundred [and] nine) is the natural number following 108 and preceding 110.

## In mathematics

109 is the 29th prime number. As 29 is itself prime, 109 is the tenth super-prime.[1] The previous prime is 107, making them both twin primes.[2]

109 is a centered triangular number.[3]

There are exactly:

• 109 different families of subsets of a three-element set whose union includes all three elements.[4]
• 109 different loops (invertible but not necessarily associative binary operations with an identity) on six elements.[5]
• 109 squares on an infinite chessboard that can be reached by a knight within three moves.[6]

There are 109 uniform edge-colorings to the 11 regular and semiregular (or Archimedean) tilings.[7]

The decimal expansion of 1/109 can be computed using the alternating series, with $\displaystyle{ F(n) }$ the $\displaystyle{ n^{th} }$ Fibonacci number:

$\displaystyle{ \frac{1}{109}=\sum_{n=1}^\infty{F(n)\times 10^{-(n+1)}}\times (-1)^{n+1}=0.00917431\dots }$

The decimal expansion of 1/109 has 108 digits, making 109 a full reptend prime in decimal. The last six digits of the 108-digit cycle are 853211, the first six Fibonacci numbers in descending order.[8]