33 (number)

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← 32 33 34 →
Cardinalthirty-three
Ordinal33rd
(thirty-third)
Factorization3 × 11
Divisors1, 3, 11, 33
Greek numeralΛΓ´
Roman numeralXXXIII
Binary1000012
Ternary10203
Quaternary2014
Quinary1135
Senary536
Octal418
Duodecimal2912
Hexadecimal2116
Vigesimal1D20
Base 36X36

33 (thirty-three) is the natural number following 32 and preceding 34.

In mathematics[edit]

33 is:

  • the largest positive integer that cannot be expressed as a sum of different triangular numbers.
  • the smallest odd repdigit that is not a prime number.
  • the sum of the first four positive factorials.
  • the sum of the sum of the divisors of the first 6 positive integers.
  • equal to the sum of the squares of the digits of its own square in bases 9, 16 and 31.
For numbers greater than 1, this is a rare property to have in more than 1 base.
  • the smallest integer such that it and the next two integers all have the same number of divisors.
  • the first member of the first cluster of three semiprimes (33, 34, 35); the next such cluster is 85, 86, 87.
  • the smallest positive integer* which has yet to be represented as a³ + b³ + c³, where a, b, and c are integers. It is conjectured that 33 can be represented this way. (*Excluding integers of the form 9k ± 4, for which solutions are known not to exist.)[1][2]

In science[edit]

  • The atomic number of arsenic
  • A normal human spine has 33 vertebrae when the bones that form the coccyx are counted individually
  • 33 is, according to the Newton scale, the temperature at which water boils.

Astronomy[edit]

In technology[edit]

In religion[edit]

In sports[edit]

In other fields[edit]

Thirty-three is:

  • A significant number in modern numerology, one of the master numbers along with 11 and 22.
  • The number printed on all Rolling Rock beer labels.
  • Pabst Blue Ribbon Beer used to be advertised as "Blended 33 to 1".
  • The namesake of the private club, Club 33, located in Disneyland's New Orleans Square.
  • The number of workers trapped, all of whom were rescued, during the 2010 Copiapó mining accident.
  • One of the symbols of Ku Klux Klan. (K is the 11th letter of the alphabet; 3 times 11 is 33, KKK).
  • The 33 Orientales were a group of Uruguay's national Independence Heroes that liberate the country in 1825 from the Brazilian Empire, the name is due for the leaders all 33 Degree Masons (The Thirty-Three Orientals), one of Uruguay's national states and its capital city is named "Treinta y Tres" after them
  • +33 is the code for international direct-dial phone calls to France.

References[edit]

  1. ^ Huisman, Sander G. (2016-04-26). "Newer sums of three cubes". arXiv:1604.07746 [math.NT].
  2. ^ Numberphile, The Uncracked Problem with 33 - Numberphile, retrieved 2018-12-12
  3. ^ Insights #517, October 8, 2010.
  4. ^ de Vries, Ad (1976). Dictionary of Symbols and Imagery. Amsterdam: North-Holland Publishing Company. p. 462. ISBN 978-0-7204-8021-4.
  5. ^ Ghazzālī; Karim, Fazlul. "Imam Gazzali's Ihya Ulum-id-din: pt. 1 and 2. The book of constructive virtues". Sind Sagar Academy. Retrieved 21 March 2018 – via Google Books.