Introduction to Prime Numbers
If a number is given and you are asked whether it is a prime number or not. What shall you do? How will you know? Do you know how to find prime numbers? So here in this article, we will be discussing what a prime number is, how to find prime numbers easily, and how to check prime numbers.
Prime numbers are the numbers which have only two factors, the number itself and 1. So we have to find such numbers which have only two factors. We will be studying various methods to find prime numbers, how to check prime numbers, and tables for prime numbers 1 to 200.
What is the Prime Number?
A prime number is an integer greater than one and can be divisible by only itself and one i.e it has only two factors. Zero, one, and numbers less than one are not considered as prime numbers.
A number having more than two factors is referred to as a composite number. The smallest prime number is 2 because it is divisible by itself and 1 only.
Finding Prime Numbers Using Factorization
The most common method used to find prime numbers is by factorization method.
The steps involved in finding prime numbers using the factorization method are:
Step 1: First let us find the factors of the given number( factors are the number which completely divides the given number)
Step 2: Then check the total number of factors of that number
Step 3: Hence, If the total number of factors is more than two, it is not a prime number but a composite number.
For Example: Take a number 45. Is it a prime number?
Factors of 45 are 5 x 3 x 3
Since the factors of 45 are more than 2 we can say that 45 is not a prime number but a composite number.
Now, if we take the example of 11. The prime factorization of 11 is 1 x 11. You can see here, there are two factors of 11. Hence, 11 is a prime number.
Methods to Find Prime Numbers
Prime numbers can also be found by the other two methods using the general formula. The methods to find prime numbers are:
Method 1:
Two consecutive numbers which are natural numbers and prime numbers are 2 and 3. Apart from 2 and 3, every prime number can be written in the form of 6n + 1 or 6n – 1, where n is a natural number.
For example:
6(1) – 1 = 5
6(1) + 1 = 7
6(2) – 1 = 11
6(2) + 1 = 13
6(3) – 1 = 17
6(3) + 1 = 19…..so on
Method 2:
To find the prime numbers greater than 40,the general formula that can be used is n2+ n + 41, where n are natural numbers 0, 1, 2, ….., 39
For example:
(0)2 + 0 + 0 = 41
(1)2 + 1 + 41 = 43
(2)2 + 2 + 41 = 47
(3)2 + 3 + 41 = 53
(4)2 + 2 + 41 = 59…..so on
Note: These both are the general formula to find the prime numbers. But values for some of them will not yield a prime number.
Table of Prime Numbers 1 to 200
Here is the list of prime numbers from 1 to 200. This table will help you to find any prime numbers 1 to 200.
List of Prime numbers from 1 to 200
Memorize this list of prime numbers from 1 to 200 and you can easily identify whether any number is prime or not.
Points to be Noted
Numbers having even numbers in one’ place cannot be a prime number.
Only 2 is an even prime number; all the rest prime numbers are odd numbers.
To find whether a larger number is prime or not, add all the digits in a number, if the sum is divisible by 3 it is not a prime number.
Except 2 and 3, all the other prime numbers can be expressed in the general form as 6n + 1 or 6n - 1, where n is the natural number.
Solved Examples
Example 1: Is 19 a Prime Number or not?
Solution:
We can check if the number is prime or not in two ways.
Method 1:
The formula for the prime number is 6n + 1
Let us write the given number in the form of 6n + 1.
6(3) + 1 = 18 + 1 = 19
Method 2:
Check for the factors of 19
19 has only two factors 1 and 19.
Therefore, by both methods, we get 19 as a prime number.
Example 2: Is 53 a prime number or not?
Solution:
Method 1:
To know the prime numbers greater than 40, the below formula can be used.
n2 + n + 41, where n = 0, 1, 2, ….., 39
Put n= 3
32 + 3 + 41 = 9 + 3 + 41 = 53
Method 2:
53 has only factors 1 and 53.
So, 53 is a prime number by both the methods.
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FAQs on How to Find Prime Numbers?
1. Check if number is prime.
The most common method used to check the prime numbers is by factorization method.
The steps involved to check prime numbers using the factorization method are:
Step 1: First let us find the factors of the given number( factors are the number that completely divides the given number)
Step 2: Then check the total number of factors of that number
- Step 3: Hence, If the total number of factors is more than two, it is not a prime number but a composite number.
2. How to calculate prime numbers?
Prime numbers can also be found by the other two methods using the general formula. The methods to find prime numbers are:
Method 1:
Two consecutive numbers which are natural numbers and prime numbers are 2 and 3. Apart from 2 and 3, every prime number can be written in the form of 6n + 1 or 6n – 1, where n is a natural number.
For example:
6(1) – 1 = 5
6(1) + 1 = 7
6(2) – 1 = 11
6(2) + 1 = 13
6(3) – 1 = 17
6(3) + 1 = 19…..so on
Method 2:
To find the prime numbers greater than 40,the general formula that can be used is n2+ n + 41, where n are natural numbers 0, 1, 2, ….., 39
For example:
(0)2 + 0 + 0 = 41
(1)2 + 1 + 41 = 43
(2)2 + 2 + 41 = 47
(3)2 + 3 + 41 = 53
(4)2 + 2 + 41 = 59…..so on
3. Is 1 a prime number or composite number?
1 is neither a prime number or a composite number because 1 is divisible by only itself, thus it has only 1 factor. Hence it contradicts both the definition of a prime number and composite number. They both have more than two factors.
4. What is the difference between prime numbers and composite numbers?
A prime number has only two factors that is the number itself and one, while a composite number has more than two factors.
A prime number is divisible by only 1 and by itself, while the composite number is divisible by all its factors.
For example, 2 is a prime number it is divisible by 1 and 2 itself
9 is a composite number, it has three factors 1, 3, and 9 and it is divisible by all its factors.
5. How is it possible to find the prime numbers among large numbers?
Prime numbers can be easily detected in various ways but finding out the larger values whether they are prime or not can be a bit hard. But you need not worry as here are some of the easiest ways to determine whether a large number is prime or not:
If there is a large number that ends with either the digits 0,2,4,6 and 8 then it is not a prime number as in all cases they are always divisible by 2
Add all the digits present in the large number and then divide it by 3. If it gets divided by 3 then the large number is not a prime number.
If the result from the above two methods goes wrong then you can take the square root of the number.
Make a list of all the prime numbers under the square root value and then divide the number that is provided by all the listed prime numbers.
If there is a number that can be easily divided by prime numbers that are less than its square root value then it cannot be considered as a prime number.
If there is any number that ends with 5 or 0 can never be a prime number as it will always be divisible by 5.
6. Why is it important to learn regarding prime numbers?
Prime numbers play an important role in arithmetic equations and hence it is important not only in Math but also in various subjects and their applications. It was also around 20,000 years ago that people started to learn about the series of prime numbers. These numbers have also been discovered by other species and have been able to adapt them for various evolution and survival reasons. It is seen that a particular species of cicadas in North America tend to follow the prime number cycle for its breeding seasons. A number such as 13 or 17 is indicated where it is after 13 years that they breed. This allows various organisms their periodic cycle to go on. Hence students can see that these are important not only in understanding Math but also in a variety of topics.
7. Is there any relationship between prime numbers and composite numbers?
Yes, there is definitely a relation between a prime number and composite numbers as they both are divisible by a certain number. However the number of factors through which they are divisible differs. For example in the case of the prime number they are divisible by only one number and the other number being itself. While in the case of composite numbers it is seen that not only does 1 and the number itself is divisible but also there are other 2 or more factors that are divisible.
8. Is it possible to use the concept of prime numbers in the real world?
Yes, it is highly possible to use prime numbers in the real world. One of the most important applications is in the cyber security field where information shared on the internet makes it safer. It is also used in various applications such as WhatsApp to encrypt the information that is being shared. It is seen that by multiplying two large numbers, there is a formation of one single large number that is very hard to decode and hence software engineers use these prime numbers to create such big codes.
9. How does Vedantu help understand the topic prime numbers and their applications?
Vedantu helps students understand the concept of prime numbers and their application in the simplest of words possible. With the help of Vedantu students get to understand how the prime number is to be found out. This helps ease out the topic even more and practice better. Students can now also access some free Vedantu revision notes that help them understand these concepts when they are entering for an exam. A glance at the notes will be more than enough to check the topic.