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.
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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
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
A composite number
can constantly be written as a product in at least two ways (since
is always possible). Call these two products
then that is obviously the case that
( divides ). Set
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
Solving for gives
It then follows that
It because of this follows that is never prime! In fact, the more general result that
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
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."
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