13 (number)

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"Thirteen" redirects here. For other uses, see 13 (disambiguation).
12 13 14
Cardinal thirteen
Ordinal 13th
(thirteenth)
Factorization prime
Prime 6th
Divisors 1, 13
Roman numeral XIII
Binary 11012
Ternary 1113
Quaternary 314
Quinary 235
Senary 216
Octal 158
Duodecimal 1112
Hexadecimal D16
Vigesimal D20
Base 36 D36

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

In spoken English, the numbers 13 and 30 are often confused. When carefully enunciated, they differ in which syllable is stressed: 13 Listeni/θərˈtn/ vs. 30 /ˈθɜrti/. However, in dates such as 1300 ("thirteen hundred") or when contrasting numbers in the teens, such as 13, 14, 15, the stress shifts to the first syllable: 13 /ˈθɜrtn/.

Strikingly similar 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[edit]

The number 13 is the sixth prime number, and the smallest emirp (a prime that is a different prime when reversed).[2] It is also a Fibonacci number, a happy number, the third centered square number, and one of only 3 known Wilson primes.

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

There are 13 Archimedean solids, and a standard torus can be sliced into 13 pieces with just 3 plane cuts.[2] 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.[3]

List of basic calculations[edit]

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 \times 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
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13
13 ^ x\, 13 169 2197 28561 371293 4826809 62748517 815730721 10604499373 137858491849 1792160394037 23298085122481 302875106592253
x ^ {13}\, 1 8192 1594323 67108864 1220703125 13060694016 96889010407 549755813888 2541865828329 10000000000000 34522712143931 106993205379072 302875106592253

Grammar[edit]

  • In all Germanic languages (such as English and German), 13 is the first compound number (in German dreizehn); the numbers 11 and 12 have their own names (in German elf and zwölf).
  • The Romance languages use different systems: In Italian, 11 is the first compound number (ùndici), while in Spanish and Portuguese, the numbers up to and including 15 (Spanish quince, Portuguese quinze), in French up to and including 16 (seize) and in Romanian up to and including 19 have their own names.
  • Like in Italian, in many other languages, 11 is the first compound number, e.g. in Arabic, Chinese, Hungarian, Japanese, Swahili.
  • Like in Romanian, in Lithuanian and most Slavic languages, excluding Russian and Polish, the numbers from 11-19 have their own names.
  • In Hindi-Urdu, nearly every number from 1–99 is irregular and must be memorized as a separate numeral.

Spelling[edit]

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.

For the English language, different systems are used: Sometimes it is recommended to spell out numbers up to and including nine or ten or twelve, like formerly in German, or even ninety-nine or one hundred. Another system spells out all numbers written in one or two words (sixteen, twenty-seven, fifteen thousand, but 372 or 15,001 ).

In religion[edit]

Roman Catholicism[edit]

The apparitions of the Virgin of Fátima in 1917 were claimed to occur on the 13th day of six consecutive months.[4]

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[5] involves praying for the saint every Tuesday over a period of thirteen weeks. Another devotion, St. Anthony's Chaplet, consists of thirteen decades of three beads each.[6]

Sikhism[edit]

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 grocery to people and when he gave groceries to the 13th person he stopped there because in Gurmukhi and Hindi the word 13 is called Terah, which means yours. And Guru Nanak Dev Ji kept on 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[edit]

Zoroastrianism[edit]

The number 13 had been considered sinister and wicked in ancient Iranian civilization and Zoroastrianism. Since beginning of the Nourooz tradition, the 13th day of each new Iranian year is called Sizdah Be-dar, and this tradition is still alive among Iranian people both within modern Iran and abroad. Since Sizdah Be-dar is the 13th day of the year, it is considered a day when evil's power might cause difficulties for people. Therefore people leave urban areas for one day and camp in the countryside. Even in the current post-1979 Revolution era, and despite the wishes of Islamic government, this tradition continues to be practiced by the majority of the population throughout Iran.

Islam[edit]

In Shia Islam 13 signifies the 13th day of the month of Rajab (Lunar calendar), which is the birth of Imam Ali. 13 also is a total of 1 Prophet and 12 Imams in the Shia school of thought.

Other[edit]

  • In Mesoamerican divination, 13 is the number of important cycles of fortune/misfortune (see Trecena).[citation needed]
  • Traditionally, there are 13 witches in a coven.[citation needed]
  • In a pentagram with a circle ratio of 13, each arm of the star equals 12.36, the number of lunar months, days and hours in a solar year. Add the arms together and you get the number of full moons in five years.[citation needed]

Lucky and unlucky[edit]

Unlucky 13[edit]

Main article: Triskaidekaphobia

The number 13 is considered an unlucky number in some countries.[7] Charles Stewart Parnell had an irrational fear of the number thirteen.[8] The end of the Mayan calendar's 13th Baktun was superstitiously feared as a harbinger of the apocalyptic 2012 phenomenon.[9] 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 labeling to avoid the number, with hotels and tall buildings being conspicuous examples (thirteenth floor).[10] It's also considered unlucky to have thirteen guests at a table. Friday the 13th has been considered the unluckiest day of the month. [7]

There is a number of theories behind the cause of the association between thirteen and bad luck, but none of them have been accepted as likely.[7]

The Last Supper[edit]

At Jesus Christ's last supper, there were thirteen people around the table, counting Christ and the twelve apostles. Some believe this unlucky because one of those thirteen, Judas Iscariot, was the betrayer of Jesus Christ.

Knights Templar[edit]

On Friday 13 October 1307, King Philip IV of France ordered the arrest of the Knights Templar.,[7] and most of the knights were tortured and killed.

Full moons[edit]

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."[11]

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.[12]

A repressed lunar cult[edit]

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.[7][13]

Lucky 13[edit]

In Italy, 13 is also considered a lucky number,[citation needed] although in Campania the expression 'tredici' (meaning 13) is said when one considers their luck to have turned for the worse.

Music[edit]

American born Horror-Punk singer and musician Joseph Poole (Murderdolls) uses the name Wednesday 13 as his stage name, taking "Wednesday" from the girl Wednesday from the Addams Family and 13 from Friday the 13th.

American country-pop singer-songwriter Taylor Swift was born on December 13. She considers 13 her lucky number due to lucky events happening to her when the number appears (her first album going gold in 13 weeks, being seated at awards shows in the 13th seat, row or section). She also wears the number written on her hand at her concerts so she has it with her everywhere she goes.

The heavy metal band, Megadeth, released their 13th studio album entitled TH1RT3EN on November 1, 2011. It consists of 13 tracks including the final song "13".

Famous American country singer and songwriter Johnny Cash first released his song called "Number Thirteen".

There are 13 notes, by inclusive counting, in a full chromatic musical octave.

Track No. 12 on American heavy metal band Danzig's album 6:66 Satan's Child is called "Thirteen".

The band Big Star wrote a song called 13.

The band XIII, Hull based thrash metal band.

The band Teenage Fanclub named their album Thirteen after Big Star's song. The band were heavily influenced by Big Star.

American alternative rock band, Pixies recorded "Number 13 Baby" for their Doolittle LP. The lyrics to the song include the line: "Standing in her chinos shirt pulled off clean, gotta tattooed tit say number 13"

English alternative rock band Blur's sixth studio album, entitled 13 was released in 1999.

The British heavy metal pioneers Black Sabbath's latest studio album is entitled 13. It was released on 11 June 2013.

Other[edit]

Colgate University also considers 13 a lucky number. They were founded in 1819 by 13 men with 13 dollars, 13 prayers and 13 articles.[14] (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 a tarot card deck, XIII is the card of Death, usually picturing the Pale horse with its rider.

A baker's dozen, devil's dozen, long dozen, or long measure is 13, one more than a standard dozen.

History[edit]

  • 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 Original 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.
  • Apollo 13 was a NASA Moon mission famous for being a "successful failure" in 1970.

In sports[edit]

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 European Super League, which uses static squad numbering.

The jersey number 13 has been retired by several North American sports teams, usually in honor of past playing greats:


In triathlon, the number 13 is not used. As such, the numbering goes 11, 12, 14, 15 under the current numbering system. The number was not used in Formula One from 1977 to 2013.

In U.S. college athletics, schools that are members of NCAA Division I are allowed to provide athletic scholarships to a maximum of 13 men's basketball players in a given season.

In rugby union, the jersey number 13 is worn by one of the two starting centres, usually the outside centre but sometimes the inside centre.

The number 13 is the most-commonly registered jersey number in modern roller derby.[15]

In TV and films[edit]

References[edit]

  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. ^ a b Wells, D. The Penguin Dictionary of Curious and Interesting Numbers, London: Penguin Group. (1987): 67–71.
  3. ^ de Koninck, J. M. (2009), Those Fascinating Numbers, American Mathematical Society, p. 4, ISBN 9780821886311 .
  4. ^ Rosemary Guiley, The Guinness Encyclopedia of Ghosts and Spirits, 1994, p. 215, ISBN 0-85112-748-7.
  5. ^ http://www.shrineofstanthony.org
  6. ^ http://www.catholicculture.org/culture
  7. ^ a b c d e http://urbanlegends.about.com/cs/historical/a/friday_the_13th.htm
  8. ^ Parnell, John Howard Charles Stewart Parnell: A Memoir New York Henry Holt and Company 1914 page 264
  9. ^ "Most Popular E-mail Newsletter". USA Today. November 24, 2011. 
  10. ^ Fleischman, Sid (August 19, 2007). "The 13th Floor: A Ghost Story". The Washington Post Company. Retrieved July 26, 2008. 
  11. ^ http://www.space.com/9566-strange-story-sunday-blue-moon.html
  12. ^ http://home.hiwaay.net/~krcool/Astro/moon/fullmoonU.htm
  13. ^ Stan Gooch, Guardians of the Ancient Wisdom (1980)
  14. ^ "Colgate: History & Traditions". Colgate University. Archived from the original on August 14, 2007. Retrieved September 1, 2007. 
  15. ^ "International Rollergirls' Master Roster". http://www.twoevils.org/rollergirls/.