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109 (number)

← 108 109 110 →
Cardinalone hundred nine
Ordinal109th
(one hundred ninth)
Factorizationprime
Prime29th
Divisors1, 109
Greek numeralΡΘ´
Roman numeralCIX
Binary11011012
Ternary110013
Quaternary12314
Quinary4145
Senary3016
Octal1558
Duodecimal9112
Hexadecimal6D16
Vigesimal5920
Base 363136

109 (one hundred [and] nine) is the natural number following 108 and preceding 110.

In mathematics

109 is the 29th prime number, so it is a prime with a prime subscript.[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] and 109 squares on an infinite chessboard that can be reached by a knight within three moves.[6]

In other fields

109 is also the atomic number of meitnerium.[7]

See also

References

  1. ^ Sloane, N.J.A. (ed.). "Sequence A006450 (Primes with prime subscripts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Sloane, N.J.A. (ed.). "Sequence A006512 (Greater of twin primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ Sloane, N.J.A. (ed.). "Sequence A005448 (Centered triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ Sloane, N.J.A. (ed.). "Sequence A003465 (Number of ways to cover an n-set)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^ Sloane, N.J.A. (ed.). "Sequence A057771 (Number of loops (quasigroups with an identity element) of order n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^ Sloane, N.J.A. (ed.). "Sequence A018836 (Number of squares on infinite chess-board at ≤ n knight's moves from a fixed square)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^ Emsley, John (2011), Nature's Building Blocks: An A-Z Guide to the Elements, Oxford University Press, p. 316, ISBN 9780199605637.