Composite number

A composite number is a natural number whose prime factorization contains at least two distinct primes or a prime several times. They are, so to speak, the counterpart to the primes. Just as a general prime elements in rings, are investigated as the whole or the Gaussian numbers, for example, there also composite numbers can be viewed.

Definition

Be and. Then there exists a (up to the order of the factors ) unique product of prime numbers, so with prime numbers, with individual primes also can appear more than once. is exactly then assembled when.

Properties

  • With the exception of the numbers zero and one, every natural number is either prime or composite.
  • Each positive even number other than two is assembled.
  • Compound numbers are referred to as primes at least the second order.
  • The numbers 0 and 1 are neither prime nor composite. While the 0 from these considerations completely brackets, it assigns 1 the empty product.
  • The sequence of composite numbers starts with: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, .. ( sequence A002808 in OEIS )

Sets

  • Fundamental Theorem of Arithmetic
  • For each composite number applies: see also set of Wilson
Integer Integer factorization Wilson's theorem
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