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Definition: Prime Numbers

A prime number or short a prime $p$ is a natural number, which has exactly two divisors, namely its trivial divisors \(1\) and \(p\).

We denote consecutive prime numbers by \(p_i, i=1,2,\ldots\) (for instance, \(p_1=2, p_2=3, p_3=5, p_4=7, p_5=11,\ldots\)) and the set of all primes as \[\mathbb P:=\{p_i,~i=1,2,\ldots\}.\]

| | | | | created: 2014-03-02 11:47:09 | modified: 2019-05-12 08:48:34 | by: bookofproofs | references: [1272]

1.Proposition: Natural Numbers and Products of Prime Numbers

2.Definition: Composite Number

3.Proposition: Existence of Prime Divisors

4.Proposition: Co-prime Primes

5.Lemma: Generalized Euclidean Lemma

6.Proposition: Greatest Common Divisors Of Integers and Prime Numbers

7.Theorem: Fundamental Theorem of Arithmetic

8.Theorem: Infinite Set of Prime Numbers

9.Definition: Perfect Square

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Bibliography (further reading)

[1272] Landau, Edmund: “Vorlesungen ├╝ber Zahlentheorie, Aus der Elementaren Zahlentheorie”, S. Hirzel, Leipzig, 1927

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