13 (number)

13 (thirteen) is the natural number following 12 and preceding 14.

For other uses, see 13 (disambiguation).

← 12 13 14 →
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Cardinalthirteen
Ordinal13th
(thirteenth)
Numeral systemtredecimal
Factorizationprime
Prime6th
Divisors1, 13
Greek numeralΙΓ´
Roman numeralXIII
Binary11012
Ternary1113
Octal158
Duodecimal1112
HexadecimalD16

Strikingly folkloric aspects of the number 13 have been noted in various cultures around the world: one theory is that this is due to the cultures employing lunar-solar calendars (there are approximately 12.41 lunations per solar year, and hence 12 "true months" plus a smaller, and often portentous, thirteenth month). This can be witnessed, for example, in the "Twelve Days of Christmas" of Western European tradition.[1]

In mathematics

The number 13 is:

  • along with 15, one of two numbers within the teen numerical range (13-19) not to use a single-digit number preceding the teen suffix; instead, it uses the adjective form of three (third) as the predecessor of said teen suffix.
  • the sixth prime number.
  • a star number[2]
  • the smallest emirp (a prime that is a different prime when its digits are reversed).[3]
  • one of only three known Wilson primes.[4]
  • a Fibonacci number.
  • a happy number.[5]
  • the third centered square number.[6]
  • a lucky number.[7]
  • equal to the sum of the squares of the digits of its own square in bases 4 and 83.
  • the smallest number whose fourth power can be written as a sum of two consecutive square numbers (1192 + 1202).

Since 52 + 122 = 132, (5, 12, 13) forms a Pythagorean triple.

There are 13 Archimedean solids as normally counted, although some include the Elongated square gyrobicupola as a fourteenth.

A standard torus can be sliced into 13 pieces with just 3 plane cuts.[3]

There are also 13 different ways for the three fastest horses in a horse race to finish, allowing for ties, a fact that can be expressed mathematically by 13 being the third ordered Bell number.[8]

List of basic calculations
Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 50 100 1000
(13)x 13 26 39 52 65 78 91 104 117 130 143 156 169 182 195 208 221 234 247 260 273 286 299 312 325 650 1300 13000
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
13 ÷ x 13 6.5 4.3 3.25 2.6 2.16 1.857142 1.625 1.4 1.3 1.18 1.083 1 0.9285714 0.86 0.8125
x ÷ 13 0.076923 0.153846 0.230769 0.307692 0.384615 0.461538 0.538461 0.615384 0.692307 0.762930 0.846153 0.923076 1 1.076923 1.153846 1.230769
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13
13x 13 169 2197 28561 371293 4826809 62748517 815730721 10604499373 137858491849 1792160394037 23298085122481 302875106592253
x13 1 8192 1594323 67108864 1220703125 13060694016 96889010407 549755813888 2541865828329 10000000000000 34522712143931 106993205379072 302875106592253

In languages

Grammar
  • In all Germanic languages, 13 is the first compound number; the numbers 11 and 12 have their own names.
  • The Romance languages use different systems: In Italian, 11 is the first compound number (undici), as in Romanian (unsprezece), while in Spanish and Portuguese, the numbers up to and including 15 (Spanish quince, Portuguese quinze), and in French up to and including 16 (seize) have their own names. This is also the case in most Slavic languages, Hindi-Urdu and other South Asian languages.

Folklore

In Germany, according to an old tradition, 13 (dreizehn), as the first compound number, was the first number written in digits; the numbers 0 (null) through 12 (zwölf) were spelled out. The Duden (the German standard dictionary) now calls this tradition (which was actually never written down as an official rule) outdated and no longer valid, but many writers still follow it.[9]

In religion

Islam

In Shia Islam, 13 signifies the 13th day of the month of Rajab (the Lunar calendar), which is the birth of Imam Ali. 13 also is a total of 1 Prophet and 12 Imams in the Islamic School of Thought. However, in Sunni Islam, the number 13 bears no symbolic significance.

Catholicism

The apparitions of the Virgin of Fátima in 1917 were claimed to occur on the 13th day of six consecutive months.[10]

In Catholic devotional practice, the number thirteen is also associated with Saint Anthony of Padua, since his feast day falls on June 13. A traditional devotion called the Thirteen Tuesdays of St. Anthony[11] involves praying to the saint every Tuesday over a period of thirteen weeks. Another devotion, St. Anthony's Chaplet, consists of thirteen decades of three beads each.[12]

Sikhism

According to famous Sakhi (Evidence) or story of Guru Nanak Dev Ji, when he was an accountant at a town of Sultanpur Lodhi, he was distributing groceries to people. When he gave groceries to the 13th person, he stopped because in Gurmukhi and Hindi the word 13 is called Terah, which means yours. And Guru Nanak Dev Ji kept saying, "Yours, yours, yours..." remembering God. People reported to the emperor that Guru Nanak Dev Ji was giving out free food to the people. When treasures were checked, there was more money than before.

The Vaisakhi, which commemorates the creation of "Khalsa" or pure Sikh was celebrated on April 13 for many years.

Judaism

Zoroastrianism

Since beginning of the Nowruz tradition, the 13th day of each new year is called Charsamba akhsami, a festival dedicated to pranks and spending time outdoors.[13]

Confucianism

Luck

Bad
Further information: Triskaidekaphobia
This elevator skips the number 13 and jumps from floor 12 to 14. The thirteenth row continues to physically exist, but is now represented by the numerical symbols for the number 14.

The number 13 is considered an unlucky number in some countries.[14] The end of the Mayan calendar's 13th Baktun was superstitiously feared as a harbinger of the apocalyptic 2012 phenomenon.[15] Fear of the number 13 has a specifically recognized phobia, triskaidekaphobia, a word coined in 1911. The superstitious sufferers of triskaidekaphobia try to avoid bad luck by keeping away from anything numbered or labelled thirteen. As a result, companies and manufacturers use another way of numbering or labelling to avoid the number, with hotels and tall buildings being conspicuous examples (thirteenth floor).[16] It is also considered unlucky to have thirteen guests at a table. Friday the 13th has been considered an unlucky day.[14]

There are a number of theories as to why the number thirteen became associated with bad luck, but none of them have been accepted as likely.[14]

  • The Last Supper: At Jesus Christ's last supper, there were thirteen people around the table, counting Christ and the twelve apostles. Some believe this is unlucky because one of those thirteen, Judas Iscariot, was the betrayer of Jesus Christ. From the 1890s, a number of English language sources relate the "unlucky" thirteen to an idea that at the Last Supper, Judas, the disciple who betrayed Jesus, was the 13th to sit at the table.[17]
  • Knights Templar: On Friday, 13 October 1307, King Philip IV of France ordered the arrest of the Knights Templar,[14] and most of the knights were tortured and killed.
  • Full Moons: A year with 13 full moons instead of 12 posed problems for the monks in charge of the calendars. "This was considered a very unfortunate circumstance, especially by the monks who had charge of the calendar of thirteen months for that year, and it upset the regular arrangement of church festivals. For this reason, thirteen came to be considered an unlucky number."[18] However, a typical century has about 37 years that have 13 full moons, compared to 63 years with 12 full moons, and typically every third or fourth year has 13 full moons.[19]
  • A Repressed Lunar Cult: In ancient cultures, the number 13 represented femininity, because it corresponded to the number of lunar (menstrual) cycles in a year (13 x 28 = 364 days). The theory is that, as the solar calendar triumphed over the lunar, the number thirteen became anathema.[14][20]
  • Hammurabi's Code: There is a myth that the earliest reference to thirteen being unlucky or evil is in the Babylonian Code of Hammurabi (circa 1780 BC), where the thirteenth law is said to be omitted. In fact, the original Code of Hammurabi has no numeration. The translation by L.W. King (1910), edited by Richard Hooker, omitted one article: If the seller have gone to (his) fate (i. e., have died), the purchaser shall recover damages in said case fivefold from the estate of the seller. Other translations of the Code of Hammurabi, for example the translation by Robert Francis Harper, include the 13th article.[21]

Good
See also: Lucky Thirteen (disambiguation)
  • France: 13 was traditionally considered a lucky number in France prior to the First World War, and was used in numerical form as a good luck symbol on postcards and charms.[22]
  • Italy: 13 was the lucky number in the Italian football pools (Totocalcio). The Italian expression "fare tredici" (literally, "make thirteen") means to hit the jackpot.[23]

Other

Colgate University also considers 13 a lucky number. They were founded in 1819 by 13 men with 13 dollars, 13 prayers and 13 articles.[24] (To this day, members of the Colgate community consider the number 13 a good omen.) In fact, the campus address is 13 Oak Drive in Hamilton, New York, and the male a cappella group is called the Colgate 13.

In the Mayan Tzolk'in calendar, trecenas mark cycles of 13-day periods. The pyramids are also set up in 9 steps divided into 7 days and 6 nights, 13 days total.

In the standard 52-card deck of playing cards there are four suits, each of 13 ranks.

A baker's dozen, devil's dozen, long dozen, or long measure is 13, one more than a standard dozen. The thirteenth loaf is called the vantage loaf because it is considered advantageous overall to get 13 loaves for the price of 12.[25]

In Arthurian legend, which was recorded in Medieval texts, King Arthur is resting in Avalon with the twelve greatest knights of the Round Table, totalling 13, and will return when his country is in peril.[26]

The Thirteen Treasures of Britain are a series of magical items listed in late Medieval texts.

The Thirteen Postures of Tai Chi are thirteen postures (consisting of Eight Gates and Five Steps) which are considered to be of fundamental importance in the practice of Tai Chi.[27]

In astronomy there are 13 star constellations in the zodiac (including Ophiuchus); this can be compared with astrology where there are 12 signs of the zodiac.

In Judaism, 13 signifies the age at which a boy matures and becomes a Bar Mitzvah, i.e., a full member of the Jewish faith (counts as a member of Minyan). The number of principles of Jewish faith according to Maimonides. According to Rabbinic commentary on the Torah, God has 13 Attributes of Mercy.

In a tarot card deck, XIII is the card of Death, usually picturing the Pale horse with its rider.

Age

History
The Great Seal of the United States features several groupings which consist of 13 things of the same type e.g. 13 olive leaves, 13 stars, 13 arrows.
  • The United States of America was created from thirteen British colonies and as such, the number thirteen is a commonly recurring motif in American heraldry. For example, there are thirteen stars on the Great Seal of the United States and there are thirteen stripes on the American flag.
    • The first flag of the United States bore thirteen stripes, alternating red and white, and thirteen white stars in the blue union. The thirteen stripes represented the Thirteen Colonies from which the United States was created, and the thirteen stars represented the number of states in the new nation. When two new states were added to the Union in 1795, the flag bore fifteen stars and fifteen stripes. With the addition of five new states in 1818, the number of stripes was re-set and permanently fixed at thirteen.
    • The Great Seal of the United States bears many images of the number thirteen, representing the Thirteen Colonies from which the United States was created. On the Seal's observe, the overhead glory bears thirteen stars. The chest shield in front of the spread eagle bears thirteen stripes (seven white and six red). In the eagle's right talon, it holds the Olive Branch of Peace, bearing thirteen olives and thirteen olive leaves. In the eagle's left talon, it holds the Weapons of War, consisting of thirteen arrows. In the eagle's mouth, it holds a scroll bearing the national motto "E Pluribus Unum" (which, by coincidence, consists of thirteen letters). On the Seal's reverse, the unfinished pyramid consists of thirteen levels.
  • The Thirteenth Amendment to the United States Constitution abolished slavery and involuntary servitude.
  • Apollo 13 was a NASA Moon mission famous for being a "successful failure" in 1970.

In sports
  • The number 13 was not used in the Indianapolis 500 from 1915 to 2002. It was not permitted for use between 1926 and 2002. In 2009, E.J. Viso, driving for HVM Racing in the 2009 IndyCar Series season, drove a green number 13 car full-time, despite terrible superstitions about it in motorsports.
  • The number 13 was not used in Formula One from 1977 to 2013.
  • In rugby league:
    • Each side has 13 players on the field at any given time.
    • The jersey number 13 is worn by the starting loose forward or lock forward in most competitions. An exception is in the Super League, which uses static squad numbering.
  • In rugby union, the jersey number 13 is worn by the outside centre.
  • In triathlon, the number 13 is not used. As such, the numbering goes 11, 12, 14, 15 under the current numbering system.
  • In Petanque, standard games are won when a team reaches the score of 13 points. A 13–0 score is called Fanny.
  • Effective with the 2020 season, Major League Baseball teams are allowed no more than 13 pitchers on their active rosters at any time during the season. The main exception is from September 1 to the end of the regular season, when this number increases to 14.
  • In NCAA Division I men's college basketball, teams are allowed to provide scholarships to no more than 13 players at any given time.

In TV, films and literature

See also

References
  1. Frazier, King of the Bean, and the Festival of Fools. Cited in Thompson, Tok. 2002. The thirteenth number: Then, there/ here and now. 'Studia Mythological Slavica 5, 145–159.
  2. https://mathworld.wolfram.com/StarNumber.html
  3. Wells, D. The Penguin Dictionary of Curious and Interesting Numbers, London: Penguin Group. (1987): 67–71.
  4. "Sloane's A007540 : Wilson primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 1, 2016.
  5. "Sloane's A007770 : Happy numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 1, 2016.
  6. "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved June 1, 2016.
  7. "A000959 Lucky numbers. (Formerly M2616 N1035)". OEIS: The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved October 31, 2018.
  8. de Koninck, J. M. (2009), Those Fascinating Numbers, American Mathematical Society, p. 4, ISBN 9780821886311
  9. "Duden | Schreibung von Zahlen bis 12". www.duden.de (in German). Retrieved March 23, 2020.
  10. Rosemary Guiley, The Guinness Encyclopedia of Ghosts and Spirits, 1994, p. 215, ISBN 0-85112-748-7.
  11. "The Shrine of St. Anthony". shrineofstanthony.org.
  12. "Liturgical Year: Prayers: Chaplet of St. Anthony". catholicculture.org.
  13. Allen, Emily; Eysenck, Juliet (April 1, 2016). "April Fool's Day: What are the best spoofs and how did it originate?". The Daily Telegraph. Retrieved June 24, 2019.
  14. Emery, David. "Why Is Friday the 13th Unlucky? - History and Folklore". About.com Entertainment.
  15. "Most Popular E-mail Newsletter". USA Today. November 24, 2011.
  16. Fleischman, Sid (August 19, 2007). "The 13th Floor: A Ghost Story". The Washington Post Company. Retrieved July 26, 2008.
  17. Cecil Adams (1992-11-06). "Why is the number 13 considered unlucky?". The Straight Dope. Retrieved 2011-05-13.
  18. "The Really Strange Story Behind Sunday's Blue Moon". Space.com.
  19. Cooley, Keith (2008). "Full Moons 1900-2100". Johns Hopkins University Applied Physics Laboratory. Archived from the original on June 24, 2011. Retrieved August 1, 2011.
  20. Stan Gooch, Guardians of the Ancient Wisdom (1980)
  21. The Code of Hammurabi (Harper translation)
  22. Owen, Davies (2018). A Supernatural War: Magic, Divination, and Faith During the First World War. Oxford: Oxford University Press. p. 136. ISBN 9780198794554.
  23. "Tredici: Definizione e significato di tredici". dizionari.corriere.it. Dizionario di Italiano il Sabatini Coletti (in Italian). Archived from the original on June 22, 2019.
  24. "Colgate: History & Traditions". Colgate University. Archived from the original on August 14, 2007. Retrieved September 1, 2007.
  25. "Vantage loaf". Oxford Reference. Oxford University Press. Retrieved July 22, 2020.
  26. Matthews, John (1991). A Glastonbury Reader. London: The Aquarian Press. p. 15. ISBN 1-85538-276-8.
  27. "The 13 Postures and 13 Principles in Tai Chi Chuan". Tai Chi and Qigong. Retrieved May 8, 2020.
  28. 13th (2016) - Ava DuVernay | Synopsis, Characteristics, Moods, Themes and Related | AllMovie, retrieved August 10, 2020
  29. Thirteen (2003) - Catherine Hardwicke | Synopsis, Characteristics, Moods, Themes and Related | AllMovie, retrieved August 10, 2020
  30. 13 Tzameti (2005) - Géla Babluani | Synopsis, Characteristics, Moods, Themes and Related | AllMovie, retrieved August 10, 2020
  31. 13 Ghosts (1960) - William Castle | Synopsis, Characteristics, Moods, Themes and Related | AllMovie, retrieved August 10, 2020
  32. Thirteen Ghosts (2001) - Steve Beck | Synopsis, Characteristics, Moods, Themes and Related | AllMovie, retrieved August 10, 2020
  33. 13 Assassins (2010) - Takashi Miike | Synopsis, Characteristics, Moods, Themes and Related | AllMovie, retrieved August 10, 2020
  34. Trinadtsat (1936) - Mikhail Romm | Synopsis, Characteristics, Moods, Themes and Related | AllMovie, retrieved August 10, 2020
  35. The 13th Warrior (1999) - John McTiernan | Synopsis, Characteristics, Moods, Themes and Related | AllMovie, retrieved August 10, 2020
  36. Apollo 13 (1995) - Ron Howard | Synopsis, Characteristics, Moods, Themes and Related | AllMovie, retrieved August 10, 2020
  37. Friday the 13th (2009) - Marcus Nispel | Synopsis, Characteristics, Moods, Themes and Related | AllMovie, retrieved August 10, 2020
  38. 13B (2009) - Vikram Kumar, Vikram Chatwal | Synopsis, Characteristics, Moods, Themes and Related | AllMovie, retrieved August 10, 2020
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