15 (number)

Mathematics

• The eighth composite number and the sixth semiprime and the first odd and fourth discrete semiprime; its proper divisors are,, and, so the first of the form, where q is a higher prime.
• a deficient number, a lucky number, a Bell number,
• the first number to be polygonal in 3 ways: it is the 5th triangular number, a hexagonal number, and pentadecagonal number.
• 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: or .

• 15's prime factors,, 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. The only other number with this property is 27.
• There are 15 truncatable primes that are both right-truncatable and left-truncatable:
• 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 is expressible in terms of square roots.
• There are 15 monohedral convex pentagonal tilings, with eight being edge-to-edge.
• There are 15 [Euclidean tilings by convex regular polygons|regular and Euclidean tilings by convex regular polygons|semiregular tilings] when infinite apeirogonal forms are counted: three are regular, eight are semiregular, and four are apeirogonal.
• Full icosahedral symmetry contains 15 mirror planes. Specifically, the symmetry order for both the regular icosahedron and regular dodecahedron 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:
• :, while, and.

Religion

Sunnism

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", because those spell out one of the Jewish names of God. Instead, the date is written with the letters representing "9" and "6".