109 (one hundred
ndnine) is the
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''Cardinal n ...
following
108 108 may refer to:
* 108 (number)
* AD 108, a year
* 108 BC, a year
* 108 (artist) (born 1978), Italian street artist
* 108 (band), an American hardcore band
* 108 (emergency telephone number), an emergency telephone number in several states in Ind ...
and preceding
110
110 may refer to:
*110 (number), natural number
*AD 110, a year
*110 BC, a year
*110 film, a cartridge-based film format used in still photography
*110 (MBTA bus), Massachusetts Bay Transportation Authority bus route
*110 (song), 2019 song by Capi ...
.
In mathematics
109 is the 29th
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
. 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, making them both
twin prime
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin p ...
s. 109 is a
centered triangular number
A centered (or centred) triangular number is a centered figurate number that represents an equilateral triangle with a dot in the center and all its other dots surrounding the center in successive equilateral triangular layers.
The followin ...
.
The decimal expansion of 1/109 can be computed using the alternating series, with
the
Fibonacci number:
::
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 mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from ...
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.
See also
*
109 (disambiguation) 109 may refer to:
* 109 (number), the integer following 108 and preceding 110
* AD 109, a year of the Julian calendar, in the second century AD
* 109 BC, a year of the pre-Julian Roman calendar
* 109 (department store), a department store in Shib ...
References
{{DEFAULTSORT:109 (Number)
Integers