109 (number)

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

← 108 109 110 →
← 100 101 102 103 104 105 106 107 108 109 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred nine
Ordinal	109th (one hundred ninth)
Factorization	prime
Prime	29th
Divisors	1, 109
Greek numeral	ΡΘ´
Roman numeral	CIX
Binary	11011012
Ternary	110013
Senary	3016
Octal	1558
Duodecimal	9112
Hexadecimal	6D16

In mathematics

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

109 is a centered triangular number.

There are exactly:

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

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

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

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

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.

Other fields

109 is also the atomic number of meitnerium.

See also

• 109 (disambiguation)