15 (number)

← 14 15 16 →
← 10 11 12 13 14 15 16 17 18 19 → List of numbers — Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	fifteen
Ordinal	15th (fifteenth)
Factorization	3 × 5
Divisors	1, 3, 5, 15
Roman numeral	XV
Binary	11112
Ternary	1203
Quaternary	334
Quinary	305
Senary	236
Octal	178
Duodecimal	1312
Hexadecimal	F16
Vigesimal	F20
Base 36	F36
Hebrew	ט"ו (Tet Vav)

15 (fifteen) 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 spoken English, the numbers 15 and 50 are often confused because they sound similar. 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/. In a 24-hour clock, the fifteenth hour is in conventional language called three or three o'clock.

In mathematics

15 is:

• a triangular number.
• a hexagonal number.^[1]
• a pentatope number.^[2]
• the 5th Bell number (i.e. the number of partitions for a set of size 4).^[3]
• the double factorial of 5.^[4]
• a composite number; its proper divisors being 1, 3 and 5.
• the number of supersingular primes.
• a repdigit in binary (1111) and quaternary (33). In hexadecimal, as well as all higher bases, 15 is represented as F.
• 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 semiprimes. The next example is the pair commencing 21.
• the smallest number that can be factorized using Shor's quantum algorithm.
• the magic constant of the unique order-3 normal magic square:

There are 15 perfect matchings of the complete graph K₆ and 15 rooted binary trees with four labeled leaves, both of these being among the types of object counted by double factorials. With only two exceptions, all prime quadruplets enclose a multiple of 15, with 15 itself being enclosed by the quadruplet (11, 13, 17, 19).

The 15 perfect matchings of K₆

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.

There are 15 solutions to Znám's problem of length 7.

Because 15 is the product of distinct Fermat primes, 3 and 5, a regular polygon with 15 sides is constructible with compass and unmarked straightedge, and cos π/15 is expressible in terms of square roots (see here).

If a positive definite quadratic form with integer matrix represents all positive integers up to 15, then it represents all positive integers via the 15 and 290 theorems.

In science

• The atomic number of phosphorus.
• Group 15 of the periodic table are sometimes known as the pnictogens.

In Pakistan

15 Madadgar is designated as an emergency number in Pakistan , 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 Sunnism

The Hanbali Sunni madhab states that the age of fifteen of a solar or lunar calendar is when one's taklif (obligation or responsibility) begins and is the stage whereby one has his deeds recorded.^[5]

In Judaism

• In the Hebrew numbering system, the number 15 is not written according to the usual method, with the letters that represent "10" and "5" (י-ה, yodh and heh), 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, teth and vav)
• Passover begins on the 15th day of the Hebrew month of Nisan
• Sukkot begins on the 15th day of the Hebrew month of Tishrei
• Tu Bishvat is a Jewish holiday occurring on the 15th of the Hebrew month of Shevat
• Shushan Purim (the day on which Purim is celebrated in Jerusalem and a few other cities in Israel) occurs on the 15th day of the Hebrew month of Adar
• Tu B'Av is a minor Jewish holiday occurring on the 15th day of the Hebrew month of Av
• There are 15 things mentioned in the middle of Yishtabach, and 15 words in the conclusion
• There are 15 Shir Hama'alot in Psalms, from 120 to 134

In sports

• In all four of the major Gaelic games—hurling, Gaelic football for men and women, and camogie—each team has 15 players on the field at any given time.
• In tennis, the number 15 represents the first point gained in a game.
• In rugby union:
  • Each team has 15 players on the field at any given time.
  • The jersey number 15 is worn by the starting fullback.
  • The Sevens World Series in rugby union sevens has had 15 "core teams" that participate in each series event since the 2012–13 season.
• In baseball, the National League and American League within Major League Baseball each have 15 teams.
• In U.S. college athletics, schools that are members of NCAA Division I are allowed to provide athletic scholarships to a maximum of 15 women's basketball players in a given season.
• The jersey number 15 has been retired by several North American sports teams in honor of past playing greats or other key figures:
  • In Major League Baseball:
    • The New York Yankees, for Thurman Munson.
  • In the NBA:
    • The Boston Celtics, for Tom Heinsohn, a member of the Naismith Memorial Basketball Hall of Fame as both a player and coach for the team.
    • The Dallas Mavericks, for Brad Davis.
    • The Detroit Pistons, for Vinnie Johnson.
    • The New York Knicks have retired the number twice, both for Hall of Fame players. #15 was first retired in 1986 for Earl Monroe. Six years later, it was retired a second time for Dick McGuire, who had worn the number before Monroe's arrival in the NBA.
    • The Philadelphia 76ers, for Hall of Famer Hal Greer.
    • The Portland Trail Blazers, for Larry Steele.
  • In the NHL:
    • The Boston Bruins, for Hall of Famer Milt Schmidt.
  • In the NFL:
    • The Green Bay Packers, for Hall of Famer Bart Starr.
    • The Philadelphia Eagles, for Hall of Famer Steve Van Buren.

Age 15

Age 15 is:

• The age of a quinceañera, a Hispanic girl celebrating her 15th 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 legal age for a driver's license is 16.
• In the UK a minor can be sent to prison to await trial at the age of 15.
• In some countries it is the legal age for sexual intercourse.^[6]
• In the UK it is the legal age to watch a BBFC "15" rated film in a cinema or purchase a "15" rated film or video game.

In other fields

Fifteen total individuals in the mollusk species Donax variabilis comprise the entire coloration and patterning in their phenotypes.

Fifteen is:

• The number of days in each of the 24 cycles of the Chinese calendar.
• The number of guns in a gun salute to Army, Marine Corps, and Air Force Lieutenant Generals, and Navy and Coast Guard Vice Admirals.
• The number of checkers each side has at the start of a backgammon game.
• The 15 puzzle.
• The number of balls in the eight ball variant of billiards
• 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.
• There are 15 Luo Points.

References

1. "Sloane's A000384 : Hexagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
2. "Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
3. "Sloane's A000110 : Bell or exponential numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
4. "Sloane's A006882 : Double factorials". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
5. Spevack, Aaron (2011). Ghazali on the Principles of Islamic Spiritualit. p. 50.
6. Worldwide Ages of Consent. Avert.org. Retrieved on 2011-11-01.

• Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 91–93

External links

• Clewett, James. "15: f in hexadecimal". Numberphile. Brady Haran. – discussing hexadecimals
• Bowley, Roger. "15: Bumfit". Numberphile. Brady Haran. – discussing the Celtic number as used in Lincolnshire