15 (number): Map

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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 vs 50 . However, in dates such as 1500 ("fifteen hundred") or when contrasting numbers in the teens, the stress generally shifts to the first syllable: 15 .

In mathematics

Fifteen is a triangular number and 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 , 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 primes.

15 is the 4th discrete biprime (3.5) and the first member of the (3.q) discrete biprime family. The number proceeding 15; 14 is itself a discrete biprime and this is the first such pair of discrete biprimes. 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 biprime 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.

In Sports

• In tennis, the number 15 represents the first point gained in a game.
• In Rugby Union the full back wears the number 15, it is also the number of players on the field.

Age 15 is:

In other fields Fifteen is:

Historical years

15 A.D., 15 B.C., 1915, 2015,

References

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

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