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: 2019-08-10 06:40:34 | by: bookofproofs | references: [1272]

1.Proposition: Existence of Prime Divisors 

2.Proposition: Natural Numbers and Products of Prime Numbers 

3.Definition: Composite Number 

4.Proposition: Co-prime Primes 

5.Lemma: Generalized Euclidean Lemma 

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

7.Definition: Perfect Square