Numbers, which don’t have any factor other than 1 or itself, are said to be prime numbers.
For example 2, 3, 5, 7, 19, 29, 31………………
Or we can say that the numbers which are not divisible by any other number except 1 and itself, are called prime numbers.
There are 25 prime numbers between 1 and 100. In general we say there are infinite prime numbers.
Prime Numbers and Composite numbers
In the list of natural numbers there are two types of natural numbers
One type is called PRIME numbers and other one is called COMPOSITE numbers.
Properties of Prime Numbers
- If p is any prime number and p divides a product of two integers say m and n i.e. p|mn (read as p divides mn), then p divides ‘m’ or p divides ‘n’ or both.
- Number of prime numbers is uncountable. i.e. there are infinite prime numbers.
- Every Prime number has exactly two factors or divisors.
For example: 13 is prime number as the divisors of 13 are 1 and 13.
- There is only one even prime i.e. 2 and all other primes are odd.
- G.C.D of prime numbers is always 1. The numbers whose G.C.D is 1 are said to be co-prime thus we say two primes are always co-prime.
- Two numbers are co-prime if their HCF is 1 .For example G.C.D. (21, 25)=1 and hence 21 and 25
are co- prime.
- The Twin Primes are pair of primes of the form (p, p+2).
- It is conjectured that there are an infinite number of twin primes.
- The term odd prime refers to any prime number greater than 2. For example: 3, 5,7, …………..
- First Prime Number is 2.
- 1 is neither prime nor composite number.
- All prime numbers greater than 3 can be expressed in the form of 6n-1 or 6n+1 i.e.
all prime numbers,which are greater than 3 leave remainder 1 or 5 when divided by 6.