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.<ref>Template:Cite OEIS</ref> The previous prime is 107, making them both twin primes.<ref>Template:Cite OEIS</ref>
109 is a centered triangular number.<ref>Template:Cite OEIS</ref>
There are exactly:
- 109 different families of subsets of a three-element set whose union includes all three elements.<ref>Template:Cite OEIS</ref>
- 109 different loops (invertible but not necessarily associative binary operations with an identity) on six elements.<ref>Template:Cite OEIS</ref>
- 109 squares on an infinite chessboard that can be reached by a knight within three moves.<ref>Template:Cite OEIS</ref>
There are 109 uniform edge-colorings to the 11 regular and semiregular (or Archimedean) tilings.<ref>Template:Cite journal</ref>
The decimal expansion of 1/109 can be computed using the alternating series, with <math>F(n)</math> the <math>n^{th}</math> Fibonacci number:
- <math>\frac{1}{109}=\sum_{n=1}^\infty{F(n)\times 10^{-(n+1)}}\times (-1)^{n+1}=0.00917431\dots</math>
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.<ref>Template:Cite web</ref>