15 (number)

15 (fifteen) is the natural number following 14 and preceding 16.

Mathematics

15 is:

• The eighth
  5, so the first of the form (3.q),^[2]
  where q is a higher prime.
• a
  binary (1111) and quaternary (33). In hexadecimal
  , and higher bases, it is represented as F.
• with an
  3
  -aliquot tree.
• the second member of the first cluster of two discrete semiprimes (14, 15); the next such cluster is (21, 22).
• the first number to be polygonal in 3 ways: it is a triangular number, a hexagonal number,^[5] and pentadecagonal number.^[6]
• a centered tetrahedral number.
• the number of partitions of
  7
  .
• the smallest number that can be factorized using Shor's quantum algorithm.
• the magic constant of the unique order-3 normal magic square.
• the number of supersingular primes.
• the smallest positive number that can be expressed as the difference of two positive squares in more than one way:^[7] ${\displaystyle 4^{2}-1^{2}}$ or ${\displaystyle 8^{2}-7^{2}}$ (see image).

Furthermore,

• 15's
  prime factors, (3 and 5), form the first twin-prime
  pair.
• The first 15 superabundant numbers are the same as the first 15 colossally abundant numbers.
• In decimal, 15 contains the digits 1 and 5 and is the result of adding together the integers from 1 to 5 (1 + 2 + 3 + 4 + 5 = 15). The only other number with this property (in decimal) is 27.
• There are 15 truncatable primes that are both right-truncatable and left-truncatable:

2, 3, 5, 7, 23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739397 (sequence A020994 in the OEIS)

• There are 15
  rooted binary trees with four labeled leaves, both of these being among the types of objects 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).
• 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.
• 15 is the product of distinct
  Fermat primes, 3 and 5; hence, a regular pentadecagon is constructible
  with a compass and unmarked straightedge, and ${\displaystyle \cos {\frac {\pi }{15}}}$ is expressible in terms of square roots.
• There are 15 monohedral convex pentagonal tilings, with eight being edge-to-edge.
• There are 15 regular and semiregular tilings when infinite (improper) apeirogonal forms are counted: three are regular (with one self-dual), eight are semiregular (with one chiral), and four are apeirogonal (from a total of 8, in-which 4 are duplicates).
• Full
  regular pentagons) is 120: equal to sum of the first 15 integers, and the factorial
  of 5, wherein the sum of the first 5 integers itself is 15. Expressed mathematically:

  ${\displaystyle \sum _{i=1}^{15}i=120}$, while ${\displaystyle \sum _{i=1}^{5}i=15}$, and ${\displaystyle 5!=120}$.

• There are 15 Archimedean solids and 15 Catalan solids when enantiomorphic forms are counted separately.
• There are 15 regular honeycombs in hyperbolic 3-space: four are compact, and 11 are paracompact.^[8]
• It is the smallest non-trivial Surprise Number. When 15 is partitioned into 2 parts of digits- smaller part 1 and larger part 5, adding numbers from smaller 1 to larger 5 = 1 + 2 + 3 + 4 + 5 = 15 = Original Number.

Science

• The atomic number of phosphorus.
• 15 Eunomia is the largest Eunomian asteroid in the inner asteroid belt.

Religion

Sunnism

The

• 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)^{[citation needed]}

References

Further reading

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

External links

Look up 15 in Wiktionary, the free dictionary.

• Clewett, James. "15: f in hexadecimal". Numberphile. Brady Haran. Archived from the original on 2013-05-16. Retrieved 2013-04-02. – discussing hexadecimals
• Bowley, Roger. "15: Bumfit". Numberphile. Brady Haran. Archived from the original on 2013-05-16. Retrieved 2013-04-01. – discussing the Celtic number as used in Lincolnshire