109 (one hundred ndnine) is the natural number following 108 and preceding 110.

In mathematics

109 is the 29th prime number. As 29 is itself prime, 109 is a

super-prime Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers. The subsequence begins :3, 5, 11, 17, 31, ...

. The previous prime is

107 107 may refer to: *107 (number), the number *AD 107, a year in the 2nd century AD *107 BC, a year in the 2nd century BC *107 (New Jersey bus) See also *10/7 (disambiguation) *Bohrium Bohrium is a synthetic chemical element with the symbol Bh a ...

, making them both twin primes. 109 is a centered triangular number. The decimal expansion of 1/109 can be computed using the alternating series, with

F(n)

the

n^

Fibonacci number: ::

\frac=\sum_^\infty\times (-1)^=0.00917431\dots

The decimal expansion of 1/109 has 108 digits, making 109 a

full reptend prime In number theory, a full reptend prime, full repetend prime, proper primeDickson, Leonard E., 1952, ''History of the Theory of Numbers, Volume 1'', Chelsea Public. Co. or long prime in base ''b'' is an odd prime number ''p'' such that the Fermat q ...

in decimal. The last six digits of the 108-digit cycle are 853211, the first six Fibonacci numbers in descending order. 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, and 109 squares on an infinite

chessboard A chessboard is a used to play chess. It consists of 64 squares, 8 rows by 8 columns, on which the chess pieces are placed. It is square in shape and uses two colours of squares, one light and one dark, in a chequered pattern. During play, the bo ...

that can be reached by a knight within three moves.

References

{{DEFAULTSORT:109 (Number) Integers