# what is the meaning of composite number

Composite Quantity

A composite quantity is a constructive integer which isn’t prime (i.e., which has components aside from 1 and itself). The primary few composite numbers (typically known as “composites” for brief) are 4, 6, 8, 9, 10, 12, 14, 15, 16, … (OEIS A002808), whose prime decompositions are summarized within the following desk. Word that the number one is a particular case which is taken into account to be neither composite nor prime.

prime factorizationprime factorization420621822924102512261427152816301832

The th composite quantity may be generated utilizing the Wolfram Language code

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Composite[n_Integer] := FixedPoint[n + PrimePi[#] + 1&, n]

The Dirichlet producing perform of the attribute perform of the composite numbers is given by

the place is the Riemann zeta perform, is the prime zeta perform, and is an Iverson bracket.

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There are an infinite variety of composite numbers.

The composite quantity downside asks if there exist constructive integers and such that .

A composite quantity can at all times be written as a product in not less than two methods (since is at all times doable). Name these two merchandise

then it’s clearly the case that ( divides ). Set

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the place is the a part of which divides , and is the a part of which divides . Then there are and such that

Fixing for provides

It then follows that

It due to this fact follows that is rarely prime! Actually, the extra common end result that

is rarely prime for an integer additionally holds (Honsberger 1991).

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