33 (number)

← 32 33 34 →
→
Cardinal	thirty-three
Ordinal	33rd (thirty-third)
Factorization	3 × 11
Divisors	1, 3, 11, 33
Greek numeral	ΛΓ´
Roman numeral	XXXIII
Binary	1000012
Ternary	10203
Senary	536
Octal	418
Duodecimal	2912
Hexadecimal	2116

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

In mathematics

33 is the 21st composite number, and 8th distinct semiprime (third of the form ${\displaystyle 3\times q}$ where ${\displaystyle q}$ is a higher prime).

).

It is the largest positive integer that cannot be expressed as a sum of different

It is also the sum of the first four positive

$${\displaystyle {\begin{aligned}33&=1!+2!+3!+4!=1+2+6+24\\33&=1+3+4+7+6+12\\\end{aligned}}}$$

It is the first member of the first cluster of three semiprimes 33, 34, 35; the next such cluster is 85, 86, 87.^[9] It is also the smallest integer such that it and the next two integers all have the same number of divisors (four).^[10]

33 is the number of unlabeled planar simple graphs with five nodes.^[11]

There are only five

); the total number of sides in these is: 3 + 4 + 6 + 8 + 12 = 33.

33 is equal to the sum of the squares of the digits of its own square in nonary (1440₉), hexadecimal (441₁₆) and unotrigesimal (144₃₁). For numbers greater than 1, this is a rare property to have in more than one base. It is also a palindrome in both decimal and binary (100001).

33 was the second to last number less than

$${\displaystyle 33=8866128975287528^{3}+(-8778405442862239)^{3}+(-2736111468807040)^{3}.}$$

Importantly, the ratio of prime numbers to non-primes at 33 in the sequence of natural numbers ${\displaystyle \mathbb {N} ^{+}}$ (up to) is ${\displaystyle {\tfrac {1}{2}}}$, where there are (inclusively) 11 prime numbers and 22 non-primes (i.e., when including 1).

Where 33 is divisible by the number of

below it (11), the product ${\displaystyle 11\times 33=363}$ is the seventh numerator of harmonic number ${\displaystyle H_{7}}$,^[13] where specifically, the previous such numerators are 49 and 137, which are respectively the thirty-third composite and prime numbers.^[14][15]

A positive definite quadratic integer matrix represents all odd numbers when it contains at least the set of seven integers: ${\displaystyle \{1,3,5,7,11,15,\mathbf {33} \}.}$^[16][17]

In science

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

Astronomy

• magnitude 7.0 galaxy in the constellation Triangulum, also known as the Triangulum Galaxy
  .
• The
  NGC 33, a double star in the constellation Pisces
• The smallest dwarf planet in the Solar System is Ceres, which is also the 33rd largest celestial body in the Solar System, comprising about one-third of the mass in the asteroid belt.^[18]
• 33 is the number of years that it takes for the
  Synodic) contains 29.53 days. A twelve-month lunar year contains 354.36 days.^[19] A solar year (Tropical year) totals 365.24 days.^[20]
  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. 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
  Islamic Calendar, the Hijri calendar based on lunar observation.^[22]

In technology

• In reference to
  45
• The ITU country code for the French telephone numbering plan area

In religion and mythology

• The number of deities in the Vedic Religion is 33.
• The second level of heaven in Buddhism is named Trāyastriṃśa, meaning "of the 33 (gods)."
• The number of incarnations the bodhisattva Avalokiteśvara is said to embody
• The divine name Elohim appears 33 times in the story of creation in the opening chapters of Genesis.^[23]
• Jewish holiday which falls on the 33rd day of the Omer
• Jesus' traditional age when he was crucified and resurrected.^[24]
• According to Al-Ghazali the dwellers of Heaven will exist eternally in a state of being age 33.^[25]
• Islamic
  names of God
  .
• Pope John Paul I, the 33-day pope. One of the shortest reigns in papal history, and it resulted in the most recent three-pope year.
• A religious image of the
  John Paul II
  in his visit to Uruguay in 1988.
  • There are several churches dedicated to this Marian devotion, including the Cathedral Basilica of Our Lady of the Thirty-Three in Florida, Uruguay.
• 33 is a master number in New Age numerology, along with 11 and 22.^[26]
• There are 33 degrees in
  Scottish Rite Freemasonry
• The
  Washington D.C.
  , US, has 33 outer columns which are each 33 feet high.
• The
  Kansai
  region of Japan.
• Rupes Nigra, a phantom island was described as having a circumference of 33 "French" miles.

In sports

• The number of innings played in the longest professional baseball game in history (a 1981 minor league game between the Rochester Red Wings and the Pawtucket Red Sox in Pawtucket, Rhode Island).^[27]
• In motorsport, 33 is the traditional number of racers in the Indianapolis 500.
• The Big 33 Football Classic is an annual postseason high school football all-star game that features top players from Pennsylvania. In recent years, the opposition has been an all-star team from Ohio. The number 33 represents the original number of players on each squad (now 34).
• FIBA 33 is the original name of the basketball variant now known as
  3x3. It is a formalized version of half-court three-on-three basketball currently being heavily promoted by the sport's international governing body, FIBA
  . Under the original rules of FIBA 33, the game ended by rule once either team scored at least 33 points, with scoring following traditional basketball rules. 3x3 uses a substantially different scoring system.
• 33 is the number of the longest winning streak in NBA History, which the Los Angeles Lakers achieved in the 1971–72 NBA Season^[28]
• World Snooker Championship semi-finals are played over 33 frames. The first rounds are played over 19 frames played in two sessions, the second round and quarter-finals played over 25 frames in three sessions, the semi-finals over 33 frames and the final over 35 frames, each played over four sessions.
• 33 was the former car number of
  Formula 1 champion Max Verstappen
  until 2022.
• An
  NFL
  is 33 yards since 2015.

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.^[29]
• 33 is the first episode of the re-imagined military science fiction television series Battlestar Galactica. The fleet are forced to execute a faster-than-light (FTL) jump every 33 minutes to evade the Cylons.

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
  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.[30]
• Georgian is presently written in a 33-letter alphabet.^[31]
• The number of bogatyrs who emerged from the sea in the Russian fairy-tale Tsar Saltan.
• The number of digits required to uniquely specify every human currently alive in binary code.

See also

• List of highways numbered 33

References

External links

• Prime Curios! 33 from the
  Prime Pages
• "33 is the sum of three cubes".
  Wolfram Alpha
  .