Definitions

# 13 (number)

"Thirteen" redirects here. For other uses of "13" and "Thirteen", see 13 (disambiguation)

13 (thirteen) is the natural number after 12 and before 14. It is the smallest integer with eight letters in its spelled out name in English. It is also the age at which children become teenagers.

## In mathematics

Thirteen is the sixth prime number; the next is seventeen. 13 is the second Wilson prime. 13 is the fifth Mersenne prime exponent, yielding 8191.

13 is the second star number and the seventh Fibonacci number. As it is an odd-indexed Fibonacci number, it is a Markov number, appearing in solutions to the "Markov Diophantine equation": (1, 5, 13), (1, 13, 34), (5, 13, 194), ...

13 is also the second happy prime, following 7, and the rethorical 1.

Thirteen is the first prime number to be the aliquot sum of two numbers; the cube 27, and the discrete biprime 35 and it is the base of the 13-aliquot tree.

There are 13 Archimedean solids.

13 goes into 999,999 exactly 76,923 times, so vulgar fractions with 13 in the denominator have six digit repeating sequences in their decimal expansions. It is thus the smallest half period prime

13 is the largest number whose factorial is less than 1010. This means 13 is often the largest factorial a pocket calculator can represent without scientific notation. (This is not really a special pure mathematical property, because it requires 10 to be the "main base number" self-evidently.)

At 13, the Mertens function sets a new low of -3, subseded later at 31 with a value of -4.

13 is the only positive integer that is the fourth root of the sum of the squares of two successive positive integers (119 and 120).

The 13th root is the most famous integer root calculation record, because 13 is the first prime number over 10 such that the last digit of a 13th integer power is the same as the last digit of its 13th root.

In base 10, the smallest prime with a composite sum of digits is 13.

13 is a repdigit in base 3 (111).

Let $_pmathrm\left\{log\right\}_gx$ denote the discrete logarithm according to the prime number $p$, i.e., the number $l$ modulo $p-1$ such that

$g^x equiv l pmod\left\{p\right\}.$
Then 13 is the only prime number $p$ such that for any two primitive roots $g$ and $h$,
$_pmathrm\left\{log\right\}_gh equiv _pmathrm\left\{log\right\}_hg pmod\left\{p-1\right\}.$

There exists an a periodic set of thirteen Wang tiles.

The Primorial+1 : 13#+1=2*3*5*7*11*13+1 is the first number of the form n#+1 which is composite.

Also, the first whole number to have the sum of its digits equal 13 and also be divisible by 13 is 247 (2+4+7=13)(13*19=247) There are 24 hours in a day and 7 days in a week. The next number to have these attributes is 364 (3+6+4)(13*28) This is one day less than a year. 13 flipped around is 31, which accounts for the number of days in most months.

## In religion

### Christianity

• There were thirteen participants at the Last Supper. Tradition states that Judas Iscariot, the disciple who betrayed Jesus, was the 13th to sit at the table.
• Thirteen was once associated with the Epiphany by Christians, as it is said the child Jesus received the Magi on his thirteenth day of life.

### 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 grocery to people and when he gave grocery to the 13th person, he stopped there because in Gurmukhi and Hindi the word 13 is called Terah which means yours. And Guru Nanak kept on saying yours yours yours remembering God. People reported to the emperor that Guru Nanak was giving out free food to the people. When treasures were checked, there was more money than before.

The word "Waheguru" appears only 13 times in Guru Granth Sahib, the Sikh holy scriptures and the eternal Guru.

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

### Other

• In Mesoamerican divination, 13 is the number of important cycles of fortune/misfortune (see Trecena).
• The number of Norse gods (there were 12) at a banquet that was crashed by the evil spirit Loki (making 13) who killed Baldr with an arrow/spear made out of mistletoe using Hodr, thus marking the beginning of Ragnarok.

### Unlucky 13

For more information, see Triskaidekaphobia.

### Lucky 13

In Sikhism, the number 13 is considered a special number since 13 is tera in Punjabi, which also means "yours" (as in, "I am yours, O Lord"). The legend goes that when Guru Nanak Dev was taking stock of items as part of his employment with a village merchant, he counted from 1 to 13 (in Punjabi) as one does normally; and thereafter he would just repeat "tera", since all items were God's creation. The merchant confronted Guru Nanak about this, but found everything to be in order after the inventory was checked. April 13 also usually turns out to be Vaisakhi every year, which is the Sikh New Year and the major Sikh Holiday.

Several successful athletes have worn the number 13. Alex Rodriguez is said to be one of the most talented baseball players ever; he has also signed the biggest sports contract and wears the number 13. Dan Marino, an American football player known for passing the 2nd most yards in NFL history, wore the number 13, although pundits in the sport have often cited him as the greatest quarterback never to win an NFL championship. Basketball great Wilt Chamberlain wore the number 13 on his jersey throughout his NBA career. Also, FIBA rules require a player to wear the number in international competitions (only numbers from 4 to 15 could be worn, and as there are 12 players, one must wear 13); Chris Mullin, who wore #20 in college and #17 in the NBA, wore #13 for both (1984 and 1992) of his Olympic appearances. Shaquille O'Neal wore #13 in 1996, Tim Duncan wore #13 in 2004, Steve Nash is currently wearing it for the Phoenix Suns, Yao Ming is currently wearing it in the 2008 Olympics in Beijing, and also Mats Sundin, wears 13 in the NHL. One of Iceland's all time best handball players, Sigurður Sveinsson, wore the number 13 when he played for the national team.

In Italy, 13 is also considered to be a lucky number.

Colgate University also considers 13 to be a lucky number. They were founded in 1819 by 13 men with 13 dollars, 13 prayers, and 13 articles. (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, NY and the all men a capella group is called the Colgate 13.

In tattoo culture, where symbols often represent the opposite of their most obvious meaning, 13 sometimes symbolizes good luck, especially in "old school" style tattoos.

## Age 13

• It is at this point when a person officially becomes a teenager.
• In Jewish tradition a boy becomes bar mitzvah at age 13, when a ceremony is held and the boy reads from the Torah for the first time. Girls may also celebrate their bat mitzvah at age 13 in many Conservative and Reform Jewish congregations.
• Youngest a minor can watch a PG-13 rated movie by the MPAA without the recommendation of parental guidance or parental consent.
• Youngest age a minor can rent or purchase a T rated game by the ESRB without parental consent.
• Minimum age a person can buy a 13+ rated movie in the Canadian province of Quebec without an adult 16 or older.

## In sports

There are 13 players in a rugby league team. In rugby union one of the centres, most often but not always the outside centre, wears the 13 shirt

Basketball Hall of Famer Wilt Chamberlain wore number 13. Three NBA teams, plus the Harlem Globetrotters, have retired his number.

Pro Football Hall of Fame quarterback Dan Marino wore number 13 for the Miami Dolphins, who retired his number in 2000.

2004-2005 and 2005-2006 NBA Most Valuable Player Steve Nash wears the number 13.

New York Jets wide receiver Don Maynard wore number 13 for the New York Jets, who retired his number in 1972.

In football (soccer), Kristine Lilly, who made more international appearances than any other player in the sport's history, wore #13 for the USA women's team. A current notable wearer of #13 in football is Michael Ballack, who wears the jersey both for his club Chelsea and the Germany national team, the latter of which he captains.

In Formula 1, no driver has had the number 13 on his car since 1976.

## In other fields

• The number of original colonies the United States was founded from. The original flag had thirteen stars, one for each state. New stars have since been added whenever a new state joins the union, but the idea of adding stripes for new states was soon dropped, so the American flag to this day has thirteen horizontal stripes: six white ones and seven red ones.
• In the Great Seal of the United States there are 13 olive leaves (with 13 olives), 13 arrows, and 13 stars. These form a triangle over the eagle with the number 13 on each point.
• The number of guns in a gun salute to U.S. Army, Air Force and Marine Corps Major Generals, and Navy and Coast Guard Rear Admirals Upper Half.
• The original number of members of The Thirteen Club.
• The number of loaves in a "baker's dozen"
• There are traditionally thirteen steps leading up to a gallows. It is, however, an urban myth that there are thirteen turns in a hangman's noose (there are most commonly eight turns.)
• Rondeau is a poem with 13 lines.
• Julius Caesar crossed the Rubicon with the 13th Legion, marking the beginning of Caesar's civil war and the eventual death of the Roman Republic.
• Trece is the Spanish word for thirteen; the number 13 is used to identify members of 13th St Sureños - chicano gang members in the U.S. that identify themselves with la Eme - the Mexican Mafia.
• There is a Latin American gang named MS-13.
• In the mythology of the television program, Battlestar Galactica, Earth is the 13th colony, lost after humanity left their planet of origin, Kobol, and created the Twelve Colonies
• In Thailand, the traditional Thai New Year (Songkran Day) is on April 13th.
• 13 steps is a paragraph of the Final Document (agreed by consensus) of the 2000 Review Conference of the Nuclear Non-Proliferation Treaty.
• In the television series House, a secretive character is nicknamed Thirteen.
• The number 1138 (1+1+3+8=13) is scattered through many of George Lucas' films, namely owing to the fact that one of his early films was THX 1138. In fact it is represented in all six of the Star Wars movies.
• there are 13 members of Organization XIII in Kingdom Hearts (series) also Roxas is the 13th member of Organization XIII.
• in fruits basket 13 members of the sohma family are cursed with the animal spirits of the Chinese Zodiac and the cat who was, according to legend, left out of the Zodiac.
• 13 is the number of the French department Bouches-du-Rhône

## Historical years

13 B.C., A.D. 13, 1913, 2013, 13th century (1201–1300), 1300s (14th century)

## References

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