Natural numbers are either prime or composite numbers. A prime number is a natural number that can only be divided by one and itself. In other words, it has exactly two factors. When we factorize a number we will write it as a multiple of prime numbers.
Examples of prime numbers:
1. The number 7 can only be divided by 1 and 7, so 7 is a prime number.
1 is not prime, since it has only one divisor, namely 1.
However, 2 and 3 are prime, since they have exactly two divisors, namely 1 and 2, and 1 and 3, respectively.
2 . Prime numbers up to 100:
2

3 
5 
7  11 
13 
17 
19 
23  29 
31 
37 
41 
43  47 
53 
59 
61 
67  71 
73 
79 
83 
89  97 
Below are the properties of prime numbers Prime numbers are uncountable. Example: 2, 3, 5, 7, .................
 Every Prime number have exactly two factors or divisors. Example: 13 is the prime number, the divisor of 13 are 1 and 13.
 Number of even primes is one. Example: 2, is a even prime number.
 G.C.D of coprime numbers is always one. Example: 5 and 7 are the coprimes G.C.D of 5 and 7 is 1.
 The general formula for generate the primes.
Formula: N = (2p −1) with p equal to the primes 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107 etc.
 The Twin Primes Conjecture that there are infinitely many pairs of primes only 2 apart.
 The term odd prime refers to any prime number greater than 2.
 All prime numbers above q are of form q $\neq$ n + m,
where 0 < m < q, and m has no prime factor less than equal to q.
 Let p is a prime number and a, b are the integers
If p divides ab, then p divides a or p divides b.