# 13 (number)

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 ← 12 13 14 →
Cardinal thirteen
Ordinal 13th
(thirteenth)
Numeral system tredecimal
Factorization prime
Prime 6th
Divisors 1, 13
Roman numeral XIII
Binary 11012
Ternary 1113
Quaternary 314
Quinary 235
Senary 216
Octal 158
Duodecimal 1112
Vigesimal D20
Base 36 D36

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

In spoken English, the numbers 13 and 30 are often confused. When carefully pronounced, they differ in which syllable is stressed: 13 vs. 30 /ˈθɜːrti/. 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 /ˈθɜːrtn/. In a 24-hour clock, the thirteenth hour is one o'clock.

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

The number 13 is:

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.[6]

### 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 (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 (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.

### Spelling

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 spelt 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

### Roman Catholicism

The apparitions of the Virgin of Fátima in 1917 were claimed to occur on the 13th day of six consecutive months.[7]

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[8] 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.[9]

### 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

• 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.

### Zoroastrianism

The number 13 had been considered sinister and wicked in ancient Iranian (Persian) 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 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

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.

### Wicca

In Wicca, most covens have 13 members, although sometimes there can be fewer.

## Lucky and unlucky

### Unlucky 13

This elevator's building and this airline both skip the number 13 and go directly from floor/row 12 to 14

The number 13 is considered an unlucky number in some countries.[10] The end of the Mayan calendar's 13th Baktun was superstitiously feared as a harbinger of the apocalyptic 2012 phenomenon.[11] 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).[12] It's also considered unlucky to have thirteen guests at a table. Friday the 13th has been considered an unlucky day. [10]

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.[10]

• 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.[13]
• Knights Templar: On Friday 13 October 1307, King Philip IV of France ordered the arrest of the Knights Templar,[10] 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."[14] 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.[15]
• 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.[10][16]
• 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.[17]
• Norse Mythology: It is believed that Loki was the 13th god in the Norse pantheon—more specifically, Loki was believed to have engineered the murder of Balder and was the 13th guest to arrive at the funeral. This is perhaps related to the superstition that if 13 people gather, one of them will die in the following year. However, the oldest source of this myth, Lokasenna, has far more than 13 guests (17 of the guests are mentioned by name) so this example should not be taken too seriously. Another Norse tradition involves the myth of Norna-Gest: When the uninvited norns showed up at his birthday celebration (thus increasing the number of guests from ten to thirteen), they cursed the infant by magically binding his lifespan to that of a mystic candle they presented to him.[18]

### Lucky 13

In many countries, such as Italy, 13 is considered a lucky number.[19] The expression fare tredici ("to do 13") means hit the jackpot. 17 is considered an unlucky number instead.[citation needed]

### Music

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 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.

The gothic metal band Type O Negative has a song titled "Thir13teen", which is the debut track of their album Life Is Killing Me.

13 is an album from the American death metal band Six Feet Under.

### 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.[20] (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.

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

A 24-hour clock uses the number 13 in the form of 13:00-13:59, to represent the fourteenth hour of its 24-hour cycle.

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

## Age 13

• 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 (is qualified to be counted as a member of Minyan).
• This is the first year a person is considered a teenager in Germanic languages, due to the suffix form beginning at this point (11 & 12 are nonstandard).
• This is also the age in the US, a person can watch, rent, or buy a PG-13 film without parental guidance.

## History

• On January 1, 49 BC, the Roman Senate issued a final order for Julius Caesar to disband his army and return to Rome because his term as governor had finished. In response, Caesar led a single legion, the Thirteenth Legion, over the Rubicon river (the frontier boundary of his Gaulish provinces to centrally administered Roman Italy). This action, in igniting Caesar's civil war, was a significant event in the eventual creation of the Roman Empire.
• On October 26, 1597 (September 13th in the Korean lunisolar calendar), Korean Admiral Yi Sun-Sin defeated a 133 warship strong Japanese naval invasion force with the last 13 ships of the Joseon navy, at the Battle of Myeongnyang. Being a decisive Joseon victory in the Myeongnyang Strait, there were no losses of any Korean ships. Later dying in the final battle of the Imjin War, Admiral Yi Sun-Sin completed his 23 battle career undefeated in combat. The surprise halt of the Japanese invasion led to a lengthy stalemate and withdrawal of the Japanese Armies from Korea, and serves as a historic foundation for Korean nationalism.
• 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.
• Apollo 13 was a NASA Moon mission famous for being a "successful failure" in 1970.

## In sports

• In boxing, after the death of boxer Duk Koo Kim following a world championship fight with World Boxing Association Lightweight champion of the world Ray Mancini (which, coincidentally, took place on November 13, 1982) the World Boxing Council determined that boxers were more likely to suffer fatal injury from round 13 to round 15, therefore soon after boxing fights were universally limited to a maximum of 12 rounds only.[21]
• 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 European 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.

## 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. ^ a b Wells, D. The Penguin Dictionary of Curious and Interesting Numbers, London: Penguin Group. (1987): 67–71.
3. ^ "Sloane's A007540 : Wilson primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
4. ^ "Sloane's A007770 : Happy numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
5. ^ "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
6. ^ de Koninck, J. M. (2009), Those Fascinating Numbers, American Mathematical Society, p. 4, ISBN 9780821886311.
7. ^ Rosemary Guiley, The Guinness Encyclopedia of Ghosts and Spirits, 1994, p. 215, ISBN 0-85112-748-7.
8. ^ "The Shrine of St. Anthony". shrineofstanthony.org.
9. ^ "Liturgical Year: Prayers: Chaplet of St. Anthony". catholicculture.org.
10. Emery, David. "Why Is Friday the 13th Unlucky? - History and Folklore". About.com Entertainment.
11. ^ "Most Popular E-mail Newsletter". USA Today. November 24, 2011.
12. ^ Fleischman, Sid (August 19, 2007). "The 13th Floor: A Ghost Story". The Washington Post Company. Retrieved July 26, 2008.
13. ^ Cecil Adams (1992-11-06). "Why is the number 13 considered unlucky?". The Straight Dope. Retrieved 2011-05-13.
14. ^
15. ^ Cooley, Keith (2008). "Full Moons 1900-2100". Johns Hopkins University Applied Physics Laboratory.
16. ^ Stan Gooch, Guardians of the Ancient Wisdom (1980)
17. ^ English translation of the Code of Hammurabi Online Library of Liberty.
18. ^ Larrington, Carolyne (Trans.) (1999). The Poetic Edda. Oxford World's Classics. ISBN 0-19-283946-2
19. ^ "Top 13 Italian Superstions". Retrieved 2015-08-13.
20. ^ "Colgate: History & Traditions". Colgate University. Archived from the original on August 14, 2007. Retrieved September 1, 2007.
21. ^ http://espn.go.com/sports/boxing/news/story?id=3107079