write program for prime number in python

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Prime Numbers Program In Python- ( Updated 2024)

What is a prime number?
Is 1 a prime number?
Co-prime numbers
Smallest and largest prime number
Python Program for prime number

Prime numbers are fascinating mathematical entities that have intrigued mathematicians for centuries. A prime number is a natural number greater than 1 that is divisible only by 1 and itself, with no other factors. These numbers possess a unique quality, making them indispensable in various fields such as cryptography, computer science, and number theory. They have a mystique that arises from their unpredictability and apparent randomness, yet they follow precise patterns and exhibit extraordinary properties. In this blog, we will explore prime numbers and delve into the implementation of a prime number program in Python. By the end, you will have a solid understanding of prime numbers and the ability to identify them using the power of programming. Let’s embark on this mathematical journey and unlock the secrets of prime numbers with Python!

Prime numbers are a subset of natural numbers whose factors are only 1 and the number itself. Why are we worried about prime numbers and obtaining prime numbers? Where can they be possibly used? We shall understand the entire concept of prime numbers in this article. Let’s get started.

The factors for a given number are those numbers that result in a zero remainder on division. These are of prime significance in the area of cryptography to enable public and private keys. Essentially, the internet is stable today because of cryptography, and this branch relies heavily on prime numbers.

Let us take a step back and pay close attention to the definition of prime numbers. They are defined as ‘the natural numbers greater than 1 that cannot be formed by multiplying two smaller natural numbers’. A natural number that is greater than 1 but is not a prime number is known as a composite number.

Therefore, we cannot include 1 in the list of prime numbers. All lists of prime numbers begin with 2. Thus, the smallest prime number is 2 and not 1.

Let us learn further. What if we have two prime numbers? What is the relationship between any two prime numbers? The greatest common divisor between two prime numbers is 1. Therefore, any pair of prime numbers results in co-primes. Co-prime numbers are the pair of numbers whose greatest common factor is 1. We can also have non-prime number pairs and prime and non-prime number pairs. For example, consider the number of pairs-

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Now that we have considered primes, what is the range of the prime numbers? We already know that the smallest prime number is 2.

What could be the largest prime number?

Well, this has some interesting trivia related to it. In the year 2018, Patrick Laroche of the Great Internet Mersenne Prime Search found the largest prime number, 282,589,933 − 1, a number which has 24,862,048 digits when written in base 10. That’s a huge number.

For now, let us focus on implementing various problems related to prime numbers. These problem statements are as follows:

Recognizing whether they are prime or not
Obtaining the set of prime numbers between a range of numbers
Recognizing whether they are prime or not.

This can be done in two ways. Let us consider the first method. Checking for all the numbers between 2 and the number itself for factors. Let us implement the same. Always start with the following algorithm-

Initialize a for loop starting from 2 and ending at the number
Check if the number is divisible by 2
Repeat till the number -1 is checked for
In case, the number is divisible by any of the numbers, the number is not prime
Else, it is a prime number

Let us consider the efficient solution, wherein we can reduce the computation into half. We check for factors only until the square root of the number. Consider 36: its factors are 1,2,3,4,6,9,12,18 and 36.

Square root of 36 is 6. Until 6, there are 4 factors apart from 1. Hence, it’s not prime.

Consider 73. Its square root is 8.5. We round it off to 9. There are no factors apart from 1 for 73 till 9. Hence it is a prime number.

Now before we get into the details of Python Program for prime number, maybe get a free refresher course on the Fundamentals of Python . This course covers all the basic and advanced concepts of Python programming like Python Data Structures, Variables, Operators, Flow Control Statements, and OOPs. It even offers a certificate on completion which could definitely boost your resume.

Let us implement the logic in python –

Initialize a for loop starting from 2 ending at the integer value of the floor of the square root of the number
Repeat till the square root of the number is checked for.

We define a function primeCheck which takes in input as the number to be checked for and returns the status. Variable sta is a variable that takes 0 or 1.

Let us consider the problem of recognizing prime numbers in a given range:

Initialize a for loop between the lower and upper ranges
Use the primeCheck function to check if the number is a prime or not
If not prime, break the loop to the next outer loop
If prime, print it.
Run the for loop till the upperRange is reached.

In this tutorial, we have covered every topic related to prime numbers. We hope you enjoyed reading the article. For more articles on machine learning and python, stay tuned!

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Python Program for Prime Number

Updated Mar 03, 2020

What is Prime Number?

A positive natural number greater than 1, which only divisible by itself and 1 is known as a prime number.

For example, 23 is a prime number because it is only divisible by 1 and itself whereas 24 is not a prime number because it is divisible by 1,2,3,4,6,8,12 and itself.

In this tutorial, you will learn how to write a python program to check whether a number is a prime number or not.

Python Program to Check Prime Number

Approach of program.

The first thing you need to check in the program is that the input variable must be greater than 1 as mentioned above prime number is greater than 1.
The second thing you need to check is if the input num is exactly divisible by any number from 2 to num - 1. If in case you find a factor in that range, then the number is not prime or else the number is prime.

1) Check Prime Number Using For Loop

Explanation

In the above code, the input() method is used for obtaining ‘num’ value from the user. We know number less than or equal to 1 are not prime numbers thus we only perform an operation on the value if ‘num’ greater than 1.

If ‘num’ is greater than 1 is true the for loop is executed. This loop checks the numbers between 2 and the number entered by the user. For every number within this range, another if statement is executed with the code if (number % i) == 0 . If this condition is True, a string is printed using the statement print(num, is not a prime number) . Otherwise, a print statement print(num, is a prime number) is printed. The last else statement is executed when the number entered is less than or equal to 1.

According to the output, the user has entered 9 as the number. As it is not a prime number, the string " 9 is not a prime number " is printed to the screen. But when 23 is entered, the string " 23 is a prime number " is printed.

2) Check Prime Number Using While Loop

In the program, the input method is used for fetching a number from the user to evaluate if it is a prime number. After converting the value to an integer, the value is stored in the variable num . Then, a variable i is assigned a value 2. The flag variable is assigned a value 0.

In the next line, A while loop is executed that runs as long as the i variable is less than the num variable. Inside the while loop, an if statement checks the modulation value of the number divided by the i variable. If the modulation value is 0, then the flag variable is assigned the value of 1. Then a break statement moves the control out of the loop.

Outside the loop, the i variable is incremented by 1. The last part of the code checks the flag value. If the value of the flag variable is equal to 0, a print statement displays "is a prime number" along with the number.

If the flag value is 1, the string "9 is not a prime number" is displayed.

So, when the user enters 9, the string is not prime a prime number” is printed. But, when the number 23 is entered, the string "23 is a prime number” is printed.

As a prime number is supposed to be a positive integer, the program checks the condition at the beginning. So, it is best to enter a positive value for checking whether it is prime or not.

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A prime number is a natural number greater than 1 and it does not have any divisor other than 1 and itself. You can write a code in Python that will help you find all the prime numbers.

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In this article, we will see how to write a prime number program in Python in the following sequence:

What is a Prime number?

Optimized Method

Let’s get started.

What is a Prime Number?

A positive integer greater than 1 which does not have other factors except 1 and the number itself is called a prime number. The numbers 2, 3, 5, 7, etc. are prime numbers as they do not have any other factors. To find a prime number in Python, you have to iterate the value from start to end using a for loop and for every number, if it is greater than 1, check if it divides n. If we find any other number which divides, print that value.

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Python Program to Check Prime Number

A prime number is always positive and it will be checked at the beginning of the program. Here, you will divide the input number by all the numbers to see whether there are any positive divisors other than 1 and number itself. If any divisor is found then we display that the “number is not a prime number” else we display that the “number is a prime number”.

Python program:

Output: 13 is a prime number

There are different ways to optimize the prime number program in Python:

Instead of checking till n, we can check till √n because a larger factor of n must be a multiple of smaller factor that has been already checked.
The algorithm can be improved further by observing that all primes are of the form 6k ± 1, with the exception of 2 and 3. This is because all integers can be expressed as (6k + i) for some integer k and for i = ?1, 0, 1, 2, 3, or 4; 2 divides (6k + 0), (6k + 2), (6k + 4); and 3 divides (6k + 3). So a more efficient method is to test if n is divisible by 2 or 3, then to check through all the numbers of form 6k ± 1.

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Python Program to Print all Prime Numbers in an Interval

To understand this example, you should have the knowledge of the following Python programming topics:

Python if...else Statement
Python for Loop
Python break and continue

A positive integer greater than 1 which has no other factors except 1 and the number itself is called a prime number.

2, 3, 5, 7 etc. are prime numbers as they do not have any other factors. But 6 is not prime (it is composite) since, 2 x 3 = 6 .

Source Code

Here, we store the interval as lower for lower interval and upper for upper interval, and find prime numbers in that range. Visit this page to learn how to check whether a number is prime or not .

Sorry about that.

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Python program to check if a number is Prime or not

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. Any whole number which is greater than 1 and has only two factors that is 1 and the number itself, is called a prime number

Let’s say the following is our input −

The output should be as follows −

Check if a number is Prime or not

Let us check if a number if a Prime number or not using the for loop −

Check if a number is Prime or not using sqrt()

Let us check if a number if a Prime number or not using the sqrt() method −

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Python Program to Check Prime Number

A prime number is a positive number that has only two factors, 1 and the number itself. Numbers such as 2, 3, 5, 7, 11, etc., are prime numbers as they do not have any other factors other than 1 and themselves. When creating the code in Python prime number that can check whether a number input is a prime number or not, the code will first check whether it is positive or not.

Prime Number Program in Python

Example 1: using a flag variable..

Here, the default value of the flag variable is set as False. When the value of the flag returns to be True, then the program breaks out of the loop. The value of the flag variable is true when the provided number gives the remainder zero with any number lesser than it and greater than zero.

Example 2: Using a for…else statement

Here, instead of using the flag variable, we set conditions using the if…else statement to check whether a number is prime or not. When no factors of the given number are found, then the number is said to be prime.

Source Code:

Python Program to check Prime Number

In the code above, all the numbers that are present between 1 and 1000 are checked to verify which are prime numbers. Note that such a code may take longer to compute, depending upon the upper and lower limit of the range between which the prime numbers need to be calculated.

To reduce the computation time of the Python prime number program to find the prime numbers that are present between a given range, the following method can be used.

In this method, we can reduce the numbers with which the given number need to be divided. It can be done by finding the root of the given number.

If the given number is divisible by any number present between 2 and its square root, then that means it is not a prime number. This happens because the square root of a number acts as a mirror between its factors. That is, the factors that lie on either side of the square root of the number are the same. Take the following example.

1 x 64 = 64

2 x 32 = 64

4 x 16 = 64

16 x 4 = 64

32 x 2 = 64

64 x 1 = 64

Here, the factors before and after 8 x 8 reflect each other.

In the code, note that we have imported the math library as we need to use the function to find the square root of the given number. The rest of the code works similarly to the ones given above. Such a code will take half the time as the original code as now the given number needs to be divided with half the numbers.

Another method to check whether a number is prime or not is to first check whether it is an even number, that is if it is divisible by 2 or not. This way, the numbers whose square root needs to be calculated will be reduced in half, further reducing the compilation and execution time of the program.

FAQs on Python Prime Number

How do you find prime numbers in Python?

To find the prime numbers in Python, the remainder of the number being divided by all numbers lying between 1 and the number itself is obtained. If any remainder is equal to zero, that means that the number is not a prime number.

Is the prime number function Python?

There is no specifically provided Python prime number provided in the Python library.

How do you find the prime number from 1 to 100 in Python?

To find all the prime numbers that lie between an upper and lower limit, such as 1 and 100, these limits will need to be defined. A FOR loop will be used to calculate the Python prime numbers that make the code iterate till the upper limit is reached. A sample code is provided below.

What is the logic of prime numbers in Python?

Using the modulus operator, it is checked if the number gives remainder zero when divided with numbers lesser than it and greater than zero.

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Python is a versatile programming language known for its simplicity and readability. It has gained immense popularity among beginners and experienced programmers alike. If you are new to coding and want to learn how to write Python code, th...
Python Program to Check Prime Number
Solve challenges and become a Python expert. A positive integer greater than 1 which has no other factors except 1 and the number itself is called a prime
Prime Numbers Program In Python- ( Updated 2024)
Python Program for prime number · Initialize a for loop starting from 2 ending at the integer value of the floor of the square root of the number
Python Program to Check Prime Number
Python Program to Check Prime Number ; num = 11. # If given number is greater than 1. if num > 1 : # Iterate from 2 to n / 2 ; from math import
Python Program for Prime Number
In the program, the input method is used for fetching a number from the user to evaluate if it is a prime number. After
How to Write a Prime Number Program in Python
The numbers 2, 3, 5, 7, etc. are prime numbers as they do not have any other factors. To find a prime number in Python, you have to iterate the
Python Program to Print all Prime Numbers in an Interval
Source code to print all prime numbers between two numbers enterd by user in Python programming with output and explanation...
Python program to check if a number is Prime or not
from math import sqrt # Number to be checked for prime n = 9 flag = 0 if(n > 1): for k in range(2, int(sqrt(n)) + 1): if (n % k == 0): flag = 1
Python Program to Print all Prime Numbers in an Interval
Python Program to Print all Prime Numbers in an Interval · # First, we will take the input: · lower_value = int(input ("Please, Enter the Lowest Range Value: "))
Prime Number Program in Python
To find prime numbers in Python, use a loop to iterate through numbers, checking each for primality by testing divisibility. Refer to the table
PRIME NUMBER PROGRAM IN PYTHON PROGRAMMING
PRIME NUMBER Number which is divisible by 1 and itself is called Prime Number if n is number n should be divided from 2 to n-1 if any number
Python Program to Check Prime Number
To find the prime numbers in Python, the remainder of the number being divided by all numbers lying between 1 and the number itself is obtained. If any

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Prime Numbers Program In Python- ( Updated 2024)

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Table of contents

Python Program for Prime Number

What is Prime Number?

Python Program to Check Prime Number

1) Check Prime Number Using For Loop

2) Check Prime Number Using While Loop

Introduction to Python

Python and Netflix: What Happens When You Stream a Film?

Python Installation

Python Fundamentals

Everything You Need To Know About Hash In Python

While Loop In Python : All You Need To Know

Python OOPs

Python Libraries

How To Make A Chatbot In Python?

Web Scraping

Python Programs

How to Find Prime Numbers in Python

Career Oppurtunities

Top Python developer Skills you need to know

Interview Questions

Data Science

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Optimized Method

What is a Prime Number?

Python Program to Check Prime Number

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Python Program to Print all Prime Numbers in an Interval

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Python program to check if a number is Prime or not

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Python Program to Check Prime Number

Prime Number Program in Python

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