# 33 (number)

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

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

## In mathematics

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 six positive integers.
• the sum of three cubes:[1] ${\displaystyle 33=8866128975287528^{3}+(-8778405442862239)^{3}+(-2736111468807040)^{3}.}$
• 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 one 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 first double digit centered dodecahedral number.
• divisible by the number of prime numbers (11) below 33.
• a palindrome in both decimal and binary.

## In science

### Astronomy

• Messier object M33, a magnitude 7.0 galaxy in the constellation Triangulum, also known as the Triangulum Galaxy.
• The New General Catalogue object NGC 33, a double star in the constellation Pisces
• 33 is the number of years that it takes for the Lunar phase to return to its original position in relation to the Solar calendar. A Lunar month (Synodic) contains 29.53 days. A twelve-month lunar year contains 354.36 days.[2] A solar year (Tropical year) totals 365.24 days.[3] The lunar year is therefore 10.88 days shorter than the 12-month solar year. As each year passes, the lunar month trails 10.88 days behind the solar year. On the turn of the 33rd year, the lunar month is approximately 359.04 days, close to one whole year behind the solar calendar from the original position measured, thus it has a 33-year cycle in relation to the solar year. The closest point at which the lunar and solar cycle meet are at 33 years and 33 weeks (calculated by dividing the 52 weeks of the 33rd year by 10.88 and multiplied by the remaining 7 day difference). Where the lunar year ${\displaystyle 354.36=l}$ and the solar year ${\displaystyle 365.24=s}$, then ${\displaystyle s-l=d}$ and ${\displaystyle 33l=33(s-d)}$. Many cultures and civilisations have based their calendar on the lunar cycles including the Athenian Attic calendar[4] and the Islamic Calendar, the Hijri calendar based on lunar observation.[5]

## In technology

• In reference to gramophone records, 33 refers to a type of record by its revolution speed of 33+13 revolutions per minute. 33s are also known as long playing records, or LPs. See: 78 and 45
• The ITU country code for the French telephone numbering plan area

## In media

• The number 33 is featured in Dark, a German science fiction television series following intertwined storylines over increments of 33 years.
• The 33 is a biographical disaster film based on the real events of a mining disaster that occurred in 2010, where a group of 33 miners became trapped inside the San José Mine in Chile.[12]

## In other fields

Thirty-three is:

• The number printed on all Rolling Rock beer labels.
• Pabst Blue Ribbon Beer used to be advertised as "Blended 33 to 1".
• The name brand of a mass-market lager beer, "33" Export, brewed and distributed in West Africa.
• 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.
• 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
• The modern Russian alphabet consists of 33 letters.[13]
• Georgian is presently written in a 33-letter alphabet.[14]

## References

1. ^ Booker, Andrew R. (2019). "Cracking the problem with 33". arXiv:1903.04284 [math.NT].
2. ^ http://adsabs.harvard.edu/full/1992JHAS...23...32S The Length of the Lunar Month, Schaefer, B. E.
3. ^ http://adsabs.harvard.edu/full/1991JRASC..85..121B The Tropical Year and Solar Calendar, Borkowski, K. M.
4. ^ worldhistory.org The Athenian Calendar
5. ^ https://eclipse.gsfc.nasa.gov/SEhelp/calendars.html Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann
6. ^ Insights #517, October 8, 2010.
7. ^ de Vries, Ad (1976). Dictionary of Symbols and Imagery. Amsterdam: North-Holland Publishing Company. pp. 462. ISBN 978-0-7204-8021-4.
8. ^ Ghazzālī; Karim, Fazlul (1978). "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.
9. ^ Sharp, Damian (2001). Simple Numerology: A Simple Wisdom book (A Simple Wisdom Book series). Red Wheel. p. 7. ISBN 978-1573245609.
10. ^ "Dedicated umpire stayed at the plate for 32 innings. - Free Online Library". www.thefreelibrary.com. Retrieved 2020-08-21.
11. ^ Cary, Tim (2015-02-14). "10 of the Longest Winning Streaks in Sports History". Sportscasting | Pure Sports. Retrieved 2020-08-21.
12. ^ "THE 33 | British Board of Film Classification". www.bbfc.co.uk. Retrieved 2020-08-21.
13. ^ "Russian Language Alphabet - listen online and practice pronunciation". Russian Step By Step Books Natasha Alexandrova. Retrieved 2020-08-21.
14. ^ "Georgian Alphabet | Georgian Language, Alphabet and Pronunciation". www.ocf.berkeley.edu. Retrieved 2020-08-21.