15 (fifteen) is the natural number following 14 and preceding 16.
Natural number
M = 15
The 15 perfect matchings of K6
15 as the difference of two positive squares (in orange).
15 is:
- The eighth composite number and the sixth semiprime and the first odd and fourth discrete semiprime;[1] its proper divisors are 1, 3, and 5, so the first of the form (3.q),[2] where q is a higher prime.
- a deficient number,[3] a lucky number, a Bell number (i.e., the number of partitions for a set of size 4),[4]
- the first number to be polygonal in 3 ways: it is the 5th triangular number,[5] a hexagonal number,[6] and pentadecagonal number.[7]
- a centered tetrahedral number.
- 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:[8]
4
2
−
1
2
{\displaystyle 4^{2}-1^{2}}
or
8
2
−
7
2
{\displaystyle 8^{2}-7^{2}}
(see image).
Furthermore,
2, 3, 5, 7, 23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739397 (sequence
A020994 in the
OEIS)
- 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 objects counted by double factorials.
- 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
cos
π
15
{\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 icosahedral symmetry contains 15 mirror planes (2-fold axes). Specifically, the symmetry order for both the regular icosahedron and regular dodecahedron (which is made of 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:
∑
i
=
1
15
i
=
120
{\displaystyle \sum _{i=1}^{15}i=120}
, while
∑
i
=
1
5
i
=
15
{\displaystyle \sum _{i=1}^{5}i=15}
, and
5
!
=
120
{\displaystyle 5!=120}
.
Seashells from the
mollusk Donax variabilis have 15 coloring pattern
phenotypes.
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.[9]
Look up
15 in Wiktionary, the free dictionary.
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400 to 999 |
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1000s and 10,000s |
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100,000s to 10,000,000,000,000s |
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- 100,000
- 1,000,000
- 10,000,000
- 100,000,000
- 1,000,000,000
- 10,000,000,000
- 100,000,000,000
- 1,000,000,000,000
- 10,000,000,000,000
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M = 15
The 15 perfect matchings of K6
15 as the difference of two positive squares (in orange).
Seashells from the mollusk Donax variabilis have 15 coloring pattern phenotypes.
