109 (number)

Template:Infobox number 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. 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:

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

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.

See also

• 109 (disambiguation)