33 (number)

"number 33" redirects here. For other uses, see 33 (disambiguation).

← 32 33 34 →
← 30 31 32 33 34 35 36 37 38 39 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
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). ^[1] It is one of two numbers to have an aliquot sum of 15 = 3 × 5 — the other being the square of 4 — and part of the aliquot sequence of 9 = 3² in the aliquot tree (33, 15, 9, 4, 3, 2, 1).

It is the largest positive integer that cannot be expressed as a sum of different triangular numbers, and it is the largest of twelve integers that are not the sum of five non-zero squares; ^[2] on the other hand, the 33rd triangular number 561 is the first Carmichael number. ^{[3] [4]} 33 is also the first non-trivial dodecagonal number (like 369, and 561) ^[5] and the first non-unitary centered dodecahedral number. ^[6]

It is also the sum of the first four positive factorials, ^[7] and the sum of the sum of the divisors of the first six positive integers; respectively: ^[8] $${\displaystyle {\begin{aligned}33&=1!+2!+3!+4!=1+2+6+24\\33&=1+3+4+7+6+12\\\end{aligned}}}$$

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 regular polygons that are used to tile the plane uniformly (the triangle, square, hexagon, octagon, and dodecagon); 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 100 whose representation as a sum of three cubes was found (in 2019): ^[12] $${\displaystyle 33=8866128975287528^{3}+(-8778405442862239)^{3}+(-2736111468807040)^{3}.}$$

33 is the sum of the only three locations ${\displaystyle n}$ in the set of integers ${\displaystyle \{1,2,3,...,n\}\in \mathbb {N} ^{+}}$ where the ratio of primes to composite numbers is one-to-one (up to ${\displaystyle n}$) — at, 9, 11, and 13; the latter two represent the fifth and sixth prime numbers, with ${\displaystyle 9=3^{2}}$ the fourth composite. On the other hand, the ratio of prime numbers to non-primes at 33 in the sequence of natural numbers ${\displaystyle \mathbb {N} ^{+}}$ is ${\displaystyle {\tfrac {1}{2}}}$, where there are (inclusively) 11 prime numbers and 22 non-primes (i.e., when including 1).

Where 33 is the seventh number divisible by the number of prime numbers below it (eleven), ^[13] the product ${\displaystyle 11\times 33=363}$ is the seventh numerator of harmonic number ${\displaystyle H_{7}}$, ^[14] where specifically, the previous such numerators are 49 and 137, which are respectively the thirty-third composite and prime numbers. ^{[15] [16]}

33 is the fifth ceiling of imaginary parts of zeros of the Riemann zeta function, that is also its nearest integer, from an approximate value of ${\displaystyle 32.93506\ldots }$ ^{[17] [18] [19] [a]}

Written in base-ten, the decimal expansion in the approximation for pi, ${\displaystyle \pi \approx 3.141592\ldots }$, has 0 as its 33rd digit, the first such single-digit string. ^{[21] [b]}

A positive definite quadratic integer matrix represents all odd numbers when it contains at least the set of seven integers: ${\displaystyle \{1,3,5,7,11,15,\mathbf {33} \}.}$ ^{[22] [23]}

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

• 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
• 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. ^[24]

In technology

• In reference to gramophone records, 33 refers to a type of record by its revolution speed of 33+1⁄3 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 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. ^[25]
• Lag Ba'omer is a minor Jewish holiday which falls on the 33rd day of the Omer
• Jesus' traditional age when he was crucified and resurrected. ^[26]
• According to Al-Ghazali the dwellers of Heaven will exist eternally in a state of being age 33. ^[27]
• Islamic prayer beads are generally arranged in sets of 33, corresponding to the widespread use of this number in dhikr rituals. Such beads may number 33 in total or three distinct sets of 33 for a total of 99, corresponding to the 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 Virgin Mary from the 18th century is known in Uruguay as "Virgen de los Treinta y Tres" (Virgin of the Thirty-Three); it was consecrated by Pope 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. ^[28]
• There are 33 degrees in Scottish Rite Freemasonry
• The House of the Temple, Home of The Supreme Council, 33°, Ancient & Accepted Scottish Rite of Freemasonry in Washington D.C., US, has 33 outer columns which are each 33 feet high.
• The Saigoku Kannon Pilgrimage visits 33 Buddhist temples throughout 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). ^[29]
• 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 ^[30]
• 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 extra point attempt in the 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. ^[31]
• 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 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. ^[32]
• Georgian is presently written in a 33-letter alphabet. ^[33]
• 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

Notes

1. These first seven digits in this approximation end in 6 and generate a sum of 28 (the seventh triangular number), numbers which represent the first and second perfect numbers, respectively (where-also, the sum between these two numbers is 34, with 35 = 7 + 28). ^[20]
2. Where 3 is the first digit of pi in decimal representation, the sum between the sixteenth and seventeenth instances (16 + 17 = 33) of a zero-string are at the 165th and 168th digits, positions whose values generate a sum of 333, and difference of 3.

References

1. Sloane, N. J. A. (ed.). "SequenceA001748". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
2. Sloane, N. J. A. (ed.). "SequenceA047701(All positive numbers that are not the sum of 5 nonzero squares.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-10-09.
3. Sloane, N. J. A. (ed.). "SequenceA000217(Triangular numbers: a(n) is the binomial(n+1,2) equal to n*(n+1)/2.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-15.
4. Sloane, N. J. A. (ed.). "SequenceA002997(Carmichael numbers: composite numbers n such that a^(n-1) congruent 1 (mod n) for every a coprime to n.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-15.
5. Sloane, N. J. A. (ed.). "SequenceA051624(12-gonal (or dodecagonal) number.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-02-24.
6. Sloane, N. J. A. (ed.). "SequenceA005904(Centered dodecahedral numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-01-12.
7. Sloane, N. J. A. (ed.). "SequenceA007489(a(n) is Sum_{k equal to 1..n} k!.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-01-12.
8. Sloane, N. J. A. (ed.). "SequenceA024916(a(n) is Sum_{k equal to 1..n} k*floor(n/k); also Sum_{k equal to 1..n} sigma(k) where sigma(n) is the sum of divisors of n (A000203).)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-01-12.
9. Sloane, N. J. A. (ed.). "SequenceA056809". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
10. Sloane, N. J. A. (ed.). "SequenceA005238(Numbers k such that k, k+1 and k+2 have the same number of divisors.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-02-27.
11. Sloane, N. J. A. (ed.). "SequenceA005470(Number of unlabeled planar simple graphs with n nodes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-01-12.
12. Booker, Andrew R. (2019). "Cracking the problem with 33". arXiv: 1903.04284 [math.NT].
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15. Sloane, N. J. A. (ed.). "SequenceA00040(The prime numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-01-12.
16. Sloane, N. J. A. (ed.). "SequenceA002808(The composite numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-01-12.
17. Sloane, N. J. A. (ed.). "SequenceA092783(Ceiling of imaginary parts of zeros of Riemann zeta function.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-06-01.
18. Sloane, N. J. A. (ed.). "SequenceA002410(Nearest integer to imaginary part of n-th zero of Riemann zeta function)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-06-02.
19. Odlyzko, Andrew. "The first 100 (non trivial) zeros of the Riemann Zeta function [AT&T Labs]". Andrew Odlyzko: Home Page. UMN CSE . Retrieved 2024-01-16.
20. Sloane, N. J. A. (ed.). "SequenceA000396(Perfect numbers k: k is equal to the sum of the proper divisors of k.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-06-02.
21. Sloane, N. J. A. (ed.). "SequenceA014976(Successive locations of zeros in decimal expansion of Pi.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-05-30.
22. Cohen, Henri (2007). "Consequences of the Hasse–Minkowski Theorem". Number Theory Volume I: Tools and Diophantine Equations. Graduate Texts in Mathematics. Vol. 239 (1st ed.). Springer. pp. 312–314. doi:10.1007/978-0-387-49923-9. ISBN   978-0-387-49922-2. OCLC   493636622. Zbl   1119.11001.
23. Sloane, N. J. A. (ed.). "SequenceA116582(Numbers from Bhargava's 33 theorem.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-10-09.
24. Williams, Matt (August 24, 2015). "What is the asteroid belt?". Phys.org . Science X. Retrieved 2023-09-22.
25. Insights #517, October 8, 2010.
26. de Vries, Ad (1976). Dictionary of Symbols and Imagery. Amsterdam: North-Holland Publishing Company. pp.  462. ISBN   978-0-7204-8021-4.
27. 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.
28. Sharp, Damian (2001). Simple Numerology: A Simple Wisdom book (A Simple Wisdom Book series). Red Wheel. p. 7. ISBN   978-1573245609.
29. "Dedicated umpire stayed at the plate for 32 innings. - Free Online Library". www.thefreelibrary.com. Retrieved 2020-08-21.
30. Cary, Tim (2015-02-14). "10 of the Longest Winning Streaks in Sports History". Sportscasting | Pure Sports. Retrieved 2020-08-21.
31. "THE 33 | British Board of Film Classification". www.bbfc.co.uk. Retrieved 2020-08-21.
32. "Russian Language Alphabet - listen online and practice pronunciation". Russian Step By Step Books Natasha Alexandrova. Retrieved 2020-08-21.
33. "Georgian Alphabet | Georgian Language, Alphabet and Pronunciation". www.ocf.berkeley.edu. Retrieved 2020-08-21.

External links

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