15 (number)
Encyclopedia
15 is the natural number
following 14
and preceding 16
. In English, it is the smallest natural number with seven letters in its spelled name.
In speech, the numbers 15 and 50 are often confused. When carefully enunciated, they differ in which syllable is stressed
: 15 fɪfˈtiːn vs 50 ˈfɪfti. However, in dates such as 1500 ("fifteen hundred") or when contrasting numbers in the teens, the stress generally shifts to the first syllable: 15 ˈfɪftiːn.
, a hexagonal number
, a pentatope number
and the 4th Bell number
. Fifteen is the double factorial of 5. It is a composite number
; its proper divisor
s being , and . With only two exceptions, all prime quadruplets enclose a multiple of 15, with 15 itself being enclosed by the quadruplet (11, 13, 17, 19). 15 is also the number of supersingular prime
s.
15 is the 4th discrete semiprime
(3.5) and the first member of the (3.q) discrete semiprime
family. It is thus the first odd discrete semiprime
. The number proceeding 15; 14
is itself a discrete semiprime
and this is the first such pair of discrete semiprime
s. The next example is the pair commencing 21
.
The aliquot sum of 15 is 9, a square prime 15 has an aliquot sequence of 6 members (15,9,4,3,1,0).
15 is the fourth composite number in the 3-aliquot tree. The abundant 12
is also a member of this tree. Fifteen is the aliquot sum of the consecutive 4-power 16, and the discrete semiprime
33.
15 and 16 form a Ruth-Aaron pair
under the second definition in which repeated prime factors are counted as often as they occur.
Fifteen is the magic constant
of the unique order-3 normal magic square
:
15 is the smallest number that can be factorized using Shor's quantum algorithm
.
There are 15 solutions to Znám's problem
of length 7.
15 is a repdigit
in binary
(1111). In hexadecimal
, as well as all higher bases, fifteen is represented as F.
, for mobile phones, similar to the international GSM emergency number 112, if 112 is used in Pakistan, then the call is routed to 15. 112 can be used in an emergency even if the phone is locked and does not have a sim-card in it.
Fifteen is:
Natural number
In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...
following 14
14 (number)
14 is the natural number following 13 and preceding 15.In speech, the numbers 14 and 40 are often confused. When carefully enunciated, they differ in which syllable is stressed: 14 vs 40...
and preceding 16
16 (number)
16 is the natural number following 15 and preceding 17. 16 is a composite number, and a square number, being 42 = 4 × 4. It is the smallest number with exactly five divisors, its proper divisors being , , and ....
. In English, it is the smallest natural number with seven letters in its spelled name.
In speech, the numbers 15 and 50 are often confused. When carefully enunciated, they differ in which syllable is stressed
Stress (linguistics)
In linguistics, stress is the relative emphasis that may be given to certain syllables in a word, or to certain words in a phrase or sentence. The term is also used for similar patterns of phonetic prominence inside syllables. The word accent is sometimes also used with this sense.The stress placed...
: 15 fɪfˈtiːn vs 50 ˈfɪfti. However, in dates such as 1500 ("fifteen hundred") or when contrasting numbers in the teens, the stress generally shifts to the first syllable: 15 ˈfɪftiːn.
In mathematics
Fifteen is a triangular numberTriangular number
A triangular number or triangle number numbers the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n...
, a hexagonal number
Hexagonal number
A hexagonal number is a figurate number. The nth hexagonal number will be the number of points in a hexagon with n regularly spaced points on a side.The formula for the nth hexagonal number...
, a pentatope number
Pentatope number
A pentatope number is a number in the fifth cell of any row of Pascal's triangle starting with the 5-term row 1 4 6 4 1 either from left to right or from right to left.The first few numbers of this kind are :...
and the 4th Bell number
Bell number
In combinatorics, the nth Bell number, named after Eric Temple Bell, is the number of partitions of a set with n members, or equivalently, the number of equivalence relations on it...
. Fifteen is the double factorial of 5. It is a composite number
Composite number
A composite number is a positive integer which has a positive divisor other than one or itself. In other words a composite number is any positive integer greater than one that is not a prime number....
; its proper divisor
Divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer which divides n without leaving a remainder.-Explanation:...
s being , and . With only two exceptions, all prime quadruplets enclose a multiple of 15, with 15 itself being enclosed by the quadruplet (11, 13, 17, 19). 15 is also the number of supersingular prime
Supersingular prime
In mathematics, a supersingular prime is a prime number satisfying one of the following concepts:*Supersingular prime , in algebraic number theory*Supersingular prime...
s.
15 is the 4th discrete semiprime
Semiprime
In mathematics, a semiprime is a natural number that is the product of two prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ... ....
(3.5) and the first member of the (3.q) discrete semiprime
Semiprime
In mathematics, a semiprime is a natural number that is the product of two prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ... ....
family. It is thus the first odd discrete semiprime
Semiprime
In mathematics, a semiprime is a natural number that is the product of two prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ... ....
. The number proceeding 15; 14
14 (number)
14 is the natural number following 13 and preceding 15.In speech, the numbers 14 and 40 are often confused. When carefully enunciated, they differ in which syllable is stressed: 14 vs 40...
is itself a discrete semiprime
Semiprime
In mathematics, a semiprime is a natural number that is the product of two prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ... ....
and this is the first such pair of discrete semiprime
Semiprime
In mathematics, a semiprime is a natural number that is the product of two prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ... ....
s. The next example is the pair commencing 21
21 (number)
21 is the natural number following 20 and preceding 22.-In mathematics:Twenty-one is the fifth discrete Semiprime and the second in the family. With 22 it forms the second discrete Semiprime pair...
.
The aliquot sum of 15 is 9, a square prime 15 has an aliquot sequence of 6 members (15,9,4,3,1,0).
15 is the fourth composite number in the 3-aliquot tree. The abundant 12
12 (number)
12 is the natural number following 11 and preceding 13.The word "twelve" is the largest number with a single-morpheme name in English. Etymology suggests that "twelve" arises from the Germanic compound twalif "two-leftover", so a literal translation would yield "two remaining [after having ten...
is also a member of this tree. Fifteen is the aliquot sum of the consecutive 4-power 16, and the discrete semiprime
Semiprime
In mathematics, a semiprime is a natural number that is the product of two prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ... ....
33.
15 and 16 form a Ruth-Aaron pair
Ruth-Aaron pair
In mathematics, a Ruth–Aaron pair consists of two consecutive integers for which the sums of the prime factors of each integer are equal:andIf only distinct prime factors are counted, the first few Ruth–Aaron pairs are:...
under the second definition in which repeated prime factors are counted as often as they occur.
Fifteen is the magic constant
Magic constant
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, and diagonal of the magic square. For example, the magic square shown below has a magic constant of 15....
of the unique order-3 normal magic square
Magic square
In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n2...
:
15 is the smallest number that can be factorized using Shor's quantum algorithm
Shor's algorithm
Shor's algorithm, named after mathematician Peter Shor, is a quantum algorithm for integer factorization formulated in 1994...
.
There are 15 solutions to Znám's problem
Znám's problem
In number theory, Znám's problem asks which sets of k integers have the property that each integer in the set is a proper divisor of the product of the other integers in the set, plus 1. Znám's problem is named after the Slovak mathematician Štefan Znám, who suggested it in 1972, although other...
of length 7.
15 is a repdigit
Repdigit
In recreational mathematics, a repdigit is a natural number composed of repeated instances of the same digit, most often in the decimal numeral system....
in binary
Binary numeral system
The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...
(1111). In hexadecimal
Hexadecimal
In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen...
, as well as all higher bases, fifteen is represented as F.
In science
- The atomic numberAtomic numberIn chemistry and physics, the atomic number is the number of protons found in the nucleus of an atom and therefore identical to the charge number of the nucleus. It is conventionally represented by the symbol Z. The atomic number uniquely identifies a chemical element...
of phosphorusPhosphorusPhosphorus is the chemical element that has the symbol P and atomic number 15. A multivalent nonmetal of the nitrogen group, phosphorus as a mineral is almost always present in its maximally oxidized state, as inorganic phosphate rocks...
. - Group 15 of the periodic tablePeriodic tableThe periodic table of the chemical elements is a tabular display of the 118 known chemical elements organized by selected properties of their atomic structures. Elements are presented by increasing atomic number, the number of protons in an atom's atomic nucleus...
are sometimes known as the "Pnictogens".
In Pakistan
15 Madadgar is designated as an emergency number in PakistanPakistan
Pakistan , officially the Islamic Republic of Pakistan is a sovereign state in South Asia. It has a coastline along the Arabian Sea and the Gulf of Oman in the south and is bordered by Afghanistan and Iran in the west, India in the east and China in the far northeast. In the north, Tajikistan...
, for mobile phones, similar to the international GSM emergency number 112, if 112 is used in Pakistan, then the call is routed to 15. 112 can be used in an emergency even if the phone is locked and does not have a sim-card in it.
In Judaism
- In the Hebrew numbering systemHebrew numeralsThe system of Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet.In this system, there is no notation for zero, and the numeric values for individual letters are added together...
, the number 15 is not written according to the usual method, with the letters that represent "10" and "5" (י-ה, yodhYodhYodh is the tenth letter of many Semitic alphabets, including Phoenician, Aramaic, Hebrew Yud , Syriac and Arabic...
and hehHe (letter)He is the fifth letter of many Semitic alphabets, including Phoenician , Aramaic, Hebrew , Syriac and Arabic . Its sound value is a voiceless glottal fricative ....
), because those spell out one of the Jewish names of God. Instead, the date is written with the letters representing "9" and "6" (ט-ו, tethTeth' is the ninth letter of many Semitic abjads , including Phoenician, Aramaic, Hebrew Tet , Syriac and Arabic ; it is 9th in abjadi order and 16th in modern Arabic order....
and vavWaw (letter)Waw is the sixth letter of the Northwest Semitic family of scripts, including Phoenician, Aramaic, Hebrew, Syriac, and Arabic ....
) - PassoverPassoverPassover is a Jewish holiday and festival. It commemorates the story of the Exodus, in which the ancient Israelites were freed from slavery in Egypt...
begins on the 15th day of the Hebrew monthHebrew calendarThe Hebrew calendar , or Jewish calendar, is a lunisolar calendar used today predominantly for Jewish religious observances. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, yahrzeits , and daily Psalm reading, among many ceremonial uses...
of NisanNisanNisan is the first month of the ecclesiastical year and the seventh month of the civil year, on the Hebrew calendar. The name of the month is Babylonian; in the Torah it is called the month of the Aviv, referring to the month in which barley was ripe. It is a spring month of 30 days... - SukkotSukkotSukkot is a Biblical holiday celebrated on the 15th day of the month of Tishrei . It is one of the three biblically mandated festivals Shalosh regalim on which Hebrews were commanded to make a pilgrimage to the Temple in Jerusalem.The holiday lasts seven days...
begins on the 15th day of the Hebrew monthHebrew calendarThe Hebrew calendar , or Jewish calendar, is a lunisolar calendar used today predominantly for Jewish religious observances. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, yahrzeits , and daily Psalm reading, among many ceremonial uses...
of TishreiTishreiTishrei or Tishri , Tiberian: ; from Akkadian "Beginning", from "To begin") is the first month of the civil year and the seventh month of the ecclesiastical year in the Hebrew calendar. The name of the month is Babylonian. It is an autumn month of 30 days... - Tu BishvatTu BishvatTu Bishvat or Tu B'Shevat is a minor Jewish holiday, occurring on the 15th day of the Hebrew month of Shevat . It is also called "The New Year of the Trees" or...
is a Jewish holidayJewish holidayJewish holidays are days observed by Jews as holy or secular commemorations of important events in Jewish history. In Hebrew, Jewish holidays and festivals, depending on their nature, may be called yom tov or chag or ta'anit...
occurring on the 15th of the Hebrew monthHebrew calendarThe Hebrew calendar , or Jewish calendar, is a lunisolar calendar used today predominantly for Jewish religious observances. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, yahrzeits , and daily Psalm reading, among many ceremonial uses...
of ShevatShevatShevat is the fifth month of the civil year and the eleventh month of the ecclesiastical year on the Hebrew calendar. It is a winter month of 30 days... - Shushan Purim (the day on which PurimPurimPurim is a Jewish holiday that commemorates the deliverance of the Jewish people in the ancient Persian Empire from destruction in the wake of a plot by Haman, a story recorded in the Biblical Book of Esther .Purim is celebrated annually according to the Hebrew calendar on the 14th...
is celebrated in Jerusalem and a few other cities in IsraelIsraelThe State of Israel is a parliamentary republic located in the Middle East, along the eastern shore of the Mediterranean Sea...
) occurs on the 15th day of the Hebrew monthHebrew calendarThe Hebrew calendar , or Jewish calendar, is a lunisolar calendar used today predominantly for Jewish religious observances. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, yahrzeits , and daily Psalm reading, among many ceremonial uses...
of AdarAdarAdar is the sixth month of the civil year and the twelfth month of the ecclesiastical year on the Hebrew calendar. It is a winter month of 29 days... - Tu B'AvTu B'AvTu B'Av is a minor Jewish holiday. In modern-day Israel, it is celebrated as a holiday of love , similar to Valentine's Day...
is a minor Jewish holidayJewish holidayJewish holidays are days observed by Jews as holy or secular commemorations of important events in Jewish history. In Hebrew, Jewish holidays and festivals, depending on their nature, may be called yom tov or chag or ta'anit...
occurring on the 15th day of the Hebrew monthHebrew calendarThe Hebrew calendar , or Jewish calendar, is a lunisolar calendar used today predominantly for Jewish religious observances. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, yahrzeits , and daily Psalm reading, among many ceremonial uses...
of Av
In sports
- In tennis, the number 15 represents the first point gained in a game.
- In Rugby UnionRugby unionRugby union, often simply referred to as rugby, is a full contact team sport which originated in England in the early 19th century. One of the two codes of rugby football, it is based on running with the ball in hand...
the full back wears the number 15, it is also the number of players on the field. - In BaseballBaseballBaseball is a bat-and-ball sport played between two teams of nine players each. The aim is to score runs by hitting a thrown ball with a bat and touching a series of four bases arranged at the corners of a ninety-foot diamond...
, New York Yankees Catcher, Thurman MunsonThurman MunsonThurman Lee Munson was an American Major League Baseball catcher. He played his entire 11-year career for the New York Yankees...
wore number 15, it was eventually retired by the Yankees organization. - In U.S. college athleticsCollege athleticsCollege athletics refers primarily to sports and athletic competition organized and funded by institutions of tertiary education . In the United States, college athletics is a two-tiered system. The first tier includes the sports that are sanctioned by one of the collegiate sport governing bodies...
, schools that are members of NCAA Division I are allowed to provide athletic scholarshipAthletic scholarshipAn athletic scholarship is a form of scholarship to attend a college or university awarded to an individual based predominantly on his or her ability to play in a sport...
s to a maximum of 15 women's basketball players in a given season.
The age 15
Age 15 is:- The age of a quinceañeraQuinceañeraQuinceañera , sometimes called "Fiesta de quince años", "Fiesta de Quinceañera", "Quince años" or simply "quince", is the celebration of a girl's fifteenth birthday in parts of Latin America and elsewhere in communities of immigrants from Latin America...
, a Hispanic girl celebrating her fifteenth birthday. Thus, Spanish bingo callers might refer to the number 15 as la niña bonita (the beautiful girl). - The age for obtaining a driver's (or learner's) permit in certain jurisdictions, including some where the age for a driver's license is sixteen16 (number)16 is the natural number following 15 and preceding 17. 16 is a composite number, and a square number, being 42 = 4 × 4. It is the smallest number with exactly five divisors, its proper divisors being , , and ....
. - In the UK a minorMinor (law)In law, a minor is a person under a certain age — the age of majority — which legally demarcates childhood from adulthood; the age depends upon jurisdiction and application, but is typically 18...
can be sent to prison to await trial at the age of 15. - In many countries it is the legal age for sexual intercourseSexual intercourseSexual intercourse, also known as copulation or coitus, commonly refers to the act in which a male's penis enters a female's vagina for the purposes of sexual pleasure or reproduction. The entities may be of opposite sexes, or they may be hermaphroditic, as is the case with snails...
. - In the UK it is the legal age to watch a BBFCBritish Board of Film ClassificationThe British Board of Film Classification , originally British Board of Film Censors, is a non-governmental organisation, funded by the film industry and responsible for the national classification of films within the United Kingdom...
"15" rated film in a cinema or purchase a "15" rated film or video game.
- The number of days in each of the 24 cycles of the Chinese calendarChinese calendarThe Chinese calendar is a lunisolar calendar, incorporating elements of a lunar calendar with those of a solar calendar. It is not exclusive to China, but followed by many other Asian cultures as well...
. - The number of guns in a gun saluteSaluteA salute is a gesture or other action used to display respect. Salutes are primarily associated with armed forces, but other organizations and civil people also use salutes.-Military salutes:...
to Army, Marine Corps, and Air Force Lieutenant Generals, and Navy and Coast Guard Vice Admirals. - The designation of Interstate 15Interstate 15Interstate 15 is the fourth-longest north–south Interstate Highway in the United States, traveling through the states of California, Nevada, Arizona, Utah, Idaho, and Montana from San Diego to the Canadian border...
, a freeway that runs from California to MontanaMontanaMontana is a state in the Western United States. The western third of Montana contains numerous mountain ranges. Smaller, "island ranges" are found in the central third of the state, for a total of 77 named ranges of the Rocky Mountains. This geographical fact is reflected in the state's name,...
. - The designation of U.S. Route 15U.S. Route 15U.S. Route 15 is a -long United States highway, designated along South Carolina, North Carolina, Virginia, Maryland, Pennsylvania, and New York. The route is signed north–south, from U.S. Route 17 Alternate in Walterboro, South Carolina to Interstate 86 and NY 17 in Painted Post, New York.US...
, a highway that runs from South CarolinaSouth CarolinaSouth Carolina is a state in the Deep South of the United States that borders Georgia to the south, North Carolina to the north, and the Atlantic Ocean to the east. Originally part of the Province of Carolina, the Province of South Carolina was one of the 13 colonies that declared independence...
to New York. - The number of checkers each side has at the start of a backgammonBackgammonBackgammon is one of the oldest board games for two players. The playing pieces are moved according to the roll of dice, and players win by removing all of their pieces from the board. There are many variants of backgammon, most of which share common traits...
game. - The 15 puzzleN-puzzleThe 15-puzzle is a sliding puzzle that consists of a frame of numbered square tiles in random order with one tile missing. The puzzle also exists in other sizes, particularly the smaller 8-puzzle...
. - A restaurant in London, built by celebrity chef Jamie OliverJamie OliverJames "Jamie" Trevor Oliver, MBE , sometimes known as The Naked Chef, is an English chef, restaurateur and media personality, known for his food-focused television shows, cookbooks and more recently his campaign against the use of processed foods in national schools...
- 15 minutes of fame15 minutes of fame15 minutes of fame is short-lived, often ephemeral, media publicity or celebrity of an individual or phenomenon. The expression was coined by Andy Warhol, who said in 1968 that "In the future, everyone will be world-famous for 15 minutes." The phenomenon is often used in reference to...
- The 15thThe 15thThe 15th is a song from the 1979 album 154 by the English rock band Wire. It was written by Colin Newman.-Fischerspooner cover:Electroclash band Fischerspooner covered The 15th as the second single from their debut album #1.-Charts:...
is a WireWire (band)Wire are an English rock band, formed in London in October 1976 by Colin Newman , Graham Lewis , Bruce Gilbert , and Robert Gotobed...
song - The number of balls in the eight ballEight ballEight-ball is a pool game popular in much of the world, and the subject of international professional and amateur competition...
variant of billiardsBilliardsCue sports , also known as billiard sports, are a wide variety of games of skill generally played with a cue stick which is used to strike billiard balls, moving them around a cloth-covered billiards table bounded by rubber .Historically, the umbrella term was billiards... - The number of letters in the words "uncopyrightable", "dermatoglyphicsDermatoglyphicsDermatoglyphics is the scientific study of fingerprints. The term was coined by Dr. Harold Cummins, the father of American fingerprint analysis, even though the process of fingerprint identification had already been in use for several hundred years. All primates have ridged skin...
", "misconjugatedly", and "hydropneumatics", which are the longest words in the English language that do not repeat a letter. - 15 is one of The Numbers – 4, 8, 15, 16, 23, and 42 – featured in LostLost (TV series)Lost is an American television series that originally aired on ABC from September 22, 2004 to May 23, 2010, consisting of six seasons. Lost is a drama series that follows the survivors of the crash of a commercial passenger jet flying between Sydney and Los Angeles, on a mysterious tropical island...
. - The number to dial for SAMUSamuSamu may refer to:* Samu, nickname for a Homo erectus man found in Vértesszőlős, Hungary* SAMU - Service d'Aide Médicale d'Urgence, an emergency medical service in France.* Servicio de Atencion Medica Urgente, also an emergency medical service...
in case of an emergency in France. - The number of minutes in one quarter of an hour; 15 minutes past or before an hour is often known as quarter past and quarter to, respectively.
- The number of the French department CantalCantalCantal is a department in south-central France. It is named after the Cantal mountain range, a group of extinct, eroded volcanic peaks, which covers much of the department. Residents are known as Cantaliens or Cantalous....
- The number corresponding to The Devil in tarotTarotThe tarot |trionfi]] and later as tarocchi, tarock, and others) is a pack of cards , used from the mid-15th century in various parts of Europe to play a group of card games such as Italian tarocchini and French tarot...
cards. - A Taylor Swift song.