*

A composite number

*
is a positive integer
*
1" /> i beg your pardon is not prime (i.e., which has components other 보다 1 and itself). The first few composite number (sometimes dubbed "composites" for short) space 4, 6, 8, 9, 10, 12, 14, 15, 16, ... (OEIS A002808), whose prime decompositions space summarized in the following table. Keep in mind that the number 1 is a special situation which is thought about to be neither composite no one prime.

You are watching: Is 15 a prime or composite number

*
prime factorization
*
prime factorization
4
*
20
*
6
*
21
*
8
*
22
*
9
*
24
*
10
*
25
*
12
*
26
*
14
*
27
*
15
*
28
*
16
*
30
*
18
*
32
*

The

*
th composite number
*
have the right to be created using the sdrta.net Language code

Composite := FixedPoint + 1&, n>The Dirichlet generating duty of the characteristic function of the composite numbers

*
is provided by

*
)/(n^s)" />
*
*

(1)
*
*
*

(2)
*
*
*

(3)

where

*
is the Riemann zeta function,
*
is the prime zeta function, and also
*
" /> is one Iverson bracket.

There are an infinite variety of composite numbers.

The composite number trouble asks if there exist confident integers

*
and also
*
such that
*
.

A composite number

*
can constantly be written as a product in at least two ways (since
*
is always possible). Call these two products


*

(4)

then that is obviously the case that

*
(
*
divides
*
). Set


*

(5)

where

*
is the part of
*
i beg your pardon divides
*
, and also
*
is the component of
*
which divides
*
. Then there room
*
and also
*
such that

*
*
*

(6)
*
*
*

(7)

Solving

*
for
*
gives


(8)

It then follows that

*
*
*

(9)
(10)
(11)

It because of this follows that

*
is never prime! In fact, the more general result that


(12)

is never prime for

*
an integer
*
=0" /> likewise holds (Honsberger 1991).


SEE ALSO: Amenable Number, Composite Number Problem, Grimm"s Conjecture, highly Composite Number, prime Factorization prime Gaps, element Number, Weakly Prime
REFERENCES:

Honsberger, R. An ext Mathematical Morsels. Washington, DC: Math. Assoc. Amer., pp.19-20, 1991.

Sloane, N.J.A. Succession A002808/M3272in "The On-Line Encyclopedia of integer Sequences."


Referenced top top sdrta.net|Alpha: Composite Number
CITE THIS AS:

Weisstein, Eric W. "Composite Number."From sdrta.net--A sdrta.net net Resource. Https://sdrta.net/CompositeNumber.html


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