15 is divisible by 1,3,5,15. So, it is not prime number.

25 prime numbers are there in between 1 and 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…………

- First arrange numbers in a table like
shown in figure.
- Enter 6 numbers in each row until the
last number (in this it is 100) reaches.
- Start with 2 which is greater than 1.
- Round off number 2 and strike off entire
column until the end.
- Similarly strike off 4
^{th}
column and 6^{th} column as they are divisible by 2.
- Now round off next number 3 and strike
off entire column until end.
- 4 is gone.
- Now round off next number 5 and strike
off numbers in inclined fashion as shown in figure. When a striking off ends in
some row, start again striking off with number in another end which is divisible by 5 in a row
parallel to previous strike off line as shown in figure.
- 6 is gone.
- Now round off number 7 and strike off
numbers as we did in case of number 5.
- 8,9,10 are gone.
- Stop at this point. Wonder why do we need
to stop??
- It’s a trick that we have to do this
procedure until we reach square root of bigger number.
- This technique was developed in 3
^{rd}
century B.C.

###
How To check if a Number is Prime

Divide the given number with every number below it except 1
and the number itself.
Check whether the given number is divisible by any of
the numbers below it.
If it is not divisible by any number then it is prime
number.

"Divisible by" means when you divide the whole number with another whole number result should be whole number with remainder zero.

Actually you don’t need to divide with all numbers.

First check whether it is divisible by 2 or not.

Next check
with 3, 5, 7, 11,13…..

Check divisibility only with prime numbers.

Here also you don’t need to divide with all prime numbers
below it.

Let p be the given number.

Find a number n greater than \(~\sqrt{p}\)

Find prime numbers below n and divide p
with only those prime numbers below n.

Actually, we used the same procedure in the above figure of finding all prime numbers upto 100.

**Ex : 1 - Number is 149**

Let us find whether 149 is prime or not.

\[\sqrt{149}= 12.20 < 13\]

prime numbers below 13 are 2,3,5,7,11….

149 is not exactly divisible by
2, because it dont has even number at end.

149 is not exactly divisible by 3, because the sum of numbers 1+4+9= 14 is not divisible by 3.

149 is not exactly divisible by 5, because it dont has 0 or 5 at end.

149 is not exactly divisible by 7,11.

So, 149 is prime number…

**Ex: 2 - number is 631**

Let us find whether 631 is prime or not.

\[\sqrt{631}= 25.11 < 26\]

prime numbers below 26 are 2,3,5,7,11,13,17,19,23….

631 is not exactly divisible by 2,3,5,7,11,13,17,19,23…
So, 631 is prime number…

For easy divisibility checking, you should know the divisibility rules.

Read about generalized divisibility rules here

###
Some Facts on Prime Numbers ** **

**Co Primes: **

H.C.F. of two numbers in one set should be 1.

Ex: (2,3),(4,5),(6,7),(11,15)

If a number N is divisible by two numbers a and b, where a,
b are co primes, then N is divisible by ab.

**Twin Primes:**

Difference between prime numbers in one set should be 2.

Ex: (3,5),(5,7),(11,13),(17,19),(31,33)

If a Number M is a prime number and N is a next prime
number, the average difference between M and N is “ ln(M) ” [natural logarithm
of M]

- 2 is the only one prime even
number.
- Numbers greater than 1 and which are not prime numbers are composite numbers.
- Some probabilistic methods are available for checking big prime numbers.

###
Prime Numbers upto 1000

Here is the list of prime numbers upto 1000 for your reference.

Thats all about Prime Numbers.

Read again about Basic Number theory
Generalized divisibility rules

check about blood relations tricks