109 (number)

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]

• 109 (disambiguation)