# Fifteen: Wikis

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# Encyclopedia

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15
Cardinal fifteen
Ordinal 15th
(fifteenth)
Factorization $3 \cdot 5$
Divisors 1, 3, 5, 15
Roman numeral XV
Binary 11112
Octal 178
Duodecimal 1312
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 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/.

## In mathematics

Fifteen is a triangular number, 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 divisors being 1, 3 and 5. 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 primes.

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 semiprimes. 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.

## The age 15

Age 15 is:

• The age of a quinceañera, 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 sixteen.
• In the UK a minor can be sent to prison to await trial at the age of 15.
• In most cultures 15 is when adulthood officially begins, from this age onwards (till 18 due to legal rights, or as a general marker into ones mid to late twenties, and sometimes early 30s.) they are called young adults.
• In Sweden and Denmark it's the legal age for sexual intercourse.
• 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:

## References

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