How To Find a Prime Number with maths aptitude tricks

                How to find if a number is prime? We get questions on this topic in some competitive exams. Deciding whether a number is prime number or not is not a simple task if it is bigger number. So, some techniques are needed to tell if the number is prime. This is what you are looking for? then you are in right place to learn how to find prime numbers easily. Because we have covered everything you need to know about Prime numbers.
Contents
1. What does prime number mean?
2. What is prime factorization – Calculating prime factors
3. Finding all prime numbers between 1 and 100 in a simple way
4. How to find a prime number – Prime number check
5. Some facts about prime numbers
6. List of all prime numbers upto 1000
 How To Find a Prime Number with aptitude tricks

What does prime number mean?

A Number which is divisible by 1 and the number itself is called as PRIME NUMBER.
Prime number must be a positive integer and it should be greater than 1.
Examples :
 
17 is divisible by 1 and 17 only, So, it is prime number.
15 is divisible by 1,3,5,15. So, it is not prime number.

What is Prime Factorization – Calculating Prime Factors

Factors of any number should be prime numbers in prime factorization.
Factors are numbers which are multiplied to get original number.
2 * 3  =  6   => 2, 3 are factors of 6. They are also prime factors of 6.
54  = 9 * 6  => 9,6 are factors of 54, but they are not prime factors.

Factor Tree :

Factor Tree can be used to get prime factors of a number.
what is prime factorization - calculating prime factors
2 * 3 * 3 * 3 = 54 => this is how we do prime factorization.

(2* (3^3)) are prime factors of 54.

List of Prime factors of numbers up to 100

List of prime factors of numbers upto 100 - maths tricks

Finding all prime numbers between 1 to 100 in a simple way

This technique can be used to find all prime numbers between any two numbers
  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…………
Finding all prime numbers between 1 and 100 in a simple way
  1. First arrange numbers in a table like shown in figure.
  2. Enter 6 numbers in each row until the last number (in this it is 100) reaches.
  3. First we select a number and we strike off all the numbers divisible by that number.
  4. Start with 2 which is greater than 1.
  5. Round off number 2 and strike off entire column until the end.
  6. Similarly strike off 4th column and 6th column as they are divisible by 2.
  7. Now round off next number 3 and strike off entire column until end.
  8. 4 is gone.
  9. Now round off next number 5 and strike off numbers in inclined fashion as shown in figure (they are divisible by 5). When striking off ends in some row, start again striking off with number in another end which is divisible by 5. new striking off line should be parallel to previous strike off line as shown in figure.
  10. 6 is gone.
  11. Now round off number 7 and strike off numbers as we did in case of number 5.
  12. 8,9,10 are gone.
  13. Stop at this point. Wonder why do we need to stop??
  14. We have to do this procedure until we reach square root of bigger number in our numbers. (in this case square root of 100 is 10)
  15. This technique was developed in 3rd century B.C.

How to find a prime number

Divide the given number with every number below it.
Check whether the given number is divisible by any of the numbers below it except 1.
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…..
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 (square root of 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.
[square root of 149= 12.20 < 13] prime numbers below 13 are 2,3,5,7,11….
149 is not exactly divisible by 2, because it don’t 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 don’t 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.
[square root of 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 non prime numbers are composite numbers.
Some probabilistic methods are available for checking big prime numbers.

List of all prime numbers upto 1000

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

 

List of all prime numbers upto 1000

Thats all about Prime Numbers.

Generalized divisibility rules

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About the author: SAI MOHAN REDDY

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