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# Python Program to Check Prime Number

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A prime number is a natural number greater than 1 that has no positive divisors other than 1 or itself. Prime numbers play a fundamental role in various areas of mathematics and computer science. In this post, we will create a Python program that gets the user’s input. If this number is a prime number, it will return true; otherwise, it will return false. Creating a Prime number program is good to start in Python.

## What is a Prime Number?

A prime number is any natural number that is greater than 1 that has no positive divisors other than 1 and itself. In simpler terms, a prime number is a whole number greater than 1 that cannot be formed by multiplying two smaller whole numbers. For example, 2,3,5,7,11, and 13 are prime numbers. These numbers are not divided by any other number except 1 and themselves.

Prime Numbers:

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, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc.

## Checking Prime Numbers in Python Program

In this Python program, we will check if the number is prime or not. The following program demonstrates the Python program.

### Program

# Python Program

```def is_prime(number): if number <= 1: return False for i in range(2, int(number**0.5) + 1): if number % i == 0: return False return True userInput = input("Enter the number from user  ") num = int(userInput) if is_prime(num): print(f"{num} is a prime number.") else: print(f"{num} is not a prime number.") ```

Output

```Enter the number from user  4 4 is not a prime number. ```

Also Read: Lambda Function in Python

## Finding Prime Number in Python using Flag Variable

In this program, we will use the flag variable to determine whether a number is prime or not. We will then print all prime numbers within a given range. In this example, we will use a loop to print the prime number.

### Program

```def is_prime(number): if number <= 1: return False for i in range(2, int(number**0.5) + 1): if number % i == 0: return False return True start = 29 end = 100 for num in range(start, end+1): if is_prime(num): print(num, end=" ") ```

Output

```29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 ```

## Check the Prime Number using the Recursion

We can also find the prime number using the recursion. Recursion is the technique where we call the function itself. The following program demonstrates the Prime Number using Recursion in Python.

### Program

```def is_prime(n, i=2): if n <= 2: return n == 2 if n % i == 0: return False if i * i > n: return True return is_prime(n, i + 1) # Python Program inputUser = input("Enter the number using the number = ") num = int(inputUser) if is_prime(num): print(f"{num} is a prime number.") else: print(f"{num} is not a prime number.") ```

### Output

```Enter the number using the number = 10 10 is not a prime number. ```

Also Read: Types of Arrays in Python

## Check the Prime Number using the while loop

In this program, we will use the while loop to check if the number is prime or not. The following program demonstrates is this number is prime or not

Program

```def is_prime_while_loop(number): if number <= 1: return False if number <= 3: return True if number % 2 == 0 or number % 3 == 0: return False i = 5 while i * i <= number: if number % i == 0 or number % (i + 2) == 0: return False i += 6 return True # Python Program inputUser = input("Enter the number = ") num = int(inputUser) if is_prime_while_loop(num): print(f"{num} is a prime number.") else: print(f"{num} is not a prime number.") ```

Output

```Enter the number = 2 2 is a prime number. ```

## Check the Prime Number using the Math module

In this program, we will use the Math module to find the prime number. If the number is prime, it will return true; otherwise, it will return false.

Progame

```import math def is_prime_check_with_math(number): if number <= 1: return False if number <= 3: return True if number % 2 == 0 or number % 3 == 0: return False for i in range(5, int(math.sqrt(number)) + 1, 6): if number % i == 0 or number % (i + 2) == 0: return False return True # Test the function inputUser = input("Enter the Number from user = ") num = int(inputUser) if is_prime_check_with_math(num): print(f"{num} is a prime number.") else: print(f"{num} is not a prime number.") ```

Output

```Enter the Number from user = 20 20 is not a prime number. ```
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## Check the Prime Number using the sympy.isprime() Method

In this program, we will use the sympy module. We can test whether a given number is prime or not using the sympy.isprime() function. The following program demonstrates the sympy.isPrime() method.

Program

```from sympy import * geek1 = isprime(30) geek2 = isprime(13) geek3 = isprime(2) print(geek1) # check for 30 is prime or not print(geek2) # check for 13 is prime or not print(geek3) # check for 2 is prime or not ```

Output

```False True True ```

## Check the Prime Number using a for…else statement

In this program, we will use the for…else statement for checking the Prime Number in Python. The following program demonstrates the for ..else loop program in Python.

Program

```def is_prime(num): if num <= 1: return False  # Not a prime number for i in range(2, int(num**0.5) + 1): if num % i == 0: return False else: return True number = int(input("Enter the number = ")) if is_prime(number): print(f"{number} is a prime number") else: print(f"{number} is not a prime number") ```

Output

```Enter the number = 23 23 is a prime number ```

## Check the Prime Number using the Trial Division Method

In this method, we will check if a number is prime by dividing it by all numbers from  2 to the square root of the number. The following program demonstrates the trial division method in the Python program.

Program

```def is_prime_trial_division(number): if number <= 1: return False if number <= 3: return True if number % 2 == 0 or number % 3 == 0: return False i = 5 while i * i <= number: if number % i == 0 or number % (i + 2) == 0: return False i += 6 return True # Test the function num = int(input("Enter the Number from the User = ")) if is_prime_trial_division(num): print(f"{num} is a prime number.") else: print(f"{num} is not a prime number.") ```

Output

```Enter the Number from the User = 2 2 is a prime number. ```

## Check the Prime Number using a Generator Function

In this program, we will check the number using the generator function in Python language. The following program demonstrates the 10 prime numbers indefinitely.

Program

```def prime_generator(): yield 2 primes = [2] current_number = 3 while True: is_prime = all(current_number % prime != 0 for prime in primes) if is_prime: primes.append(current_number) yield current_number current_number += 2 generator = prime_generator() for _ in range(10): print(next(generator)) ```

Output

```2 3 5 7 11 13 17 19 23 29 ```

## Prime Factorization

In this program, we will find the prime factorisation of a number taken from the user. The following program demonstrates the Prime factorisation.

Program

```def prime_factors(n): factors = [] divisor = 2 while n > 1: while n % divisor == 0: factors.append(divisor) n //= divisor divisor += 1 return factors number = int(input("Enter the number from the user = ")) factors = prime_factors(number) print(f"Prime factors of {number}: {factors}") ```

Output

```Enter the number from the user = 15 Prime factors of 15: [3, 5] ```

## Sieve of Eratosthenes

The sieve of Eratosthenes is an algorithm for finding a prime number at a given limit. It was developed by the Greek astronomer Eratosthenes and is a very simple algorithm for computing the prime number.

The following program demonstrates this algorithm example.

Program

```def sieve_of_eratosthenes(limit): sieve = [True] * (limit + 1) sieve[0:2] = [False, False] p = 2 while p * p <= limit: if sieve[p]: for i in range(p * p, limit + 1, p): sieve[i] = False p += 1 primes = [i for i, is_prime in enumerate(sieve) if is_prime] return primes # Find and print all prime numbers up to 50 limit = int(input("Enter the limit of the number = ")) primes = sieve_of_eratosthenes(limit) print(f"Prime numbers up to {limit}: {primes}") ```

Output

```Enter the limit of the number = 30 Prime numbers up to 30: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29] ```

## Conclusion

In this article, we learned various techniques to find prime numbers in the Python programming language, such as Using the Math module, the while loop, and the Sympy module. Each method has its own advantages and use cases. Prime numbers, the building blocks of number theory, hold a central position in mathematics and commute science. If you want to explore Python language, check out the Accelerator Program in Business Analytics and Data Science.

FAQs
In the Python Program, we can find the prime number between 1 and 100 using a function. This function uses a loop internally to find the prime number between 1 and 100.
The Python programming language includes the sympy library. In this library, we have the ‘isPrime()’ method for checking whether a number is prime or not. If this number is Prime, it will return true; otherwise, it will return false.
The most efficient way to find the prime number in Python using by algorithm like the Sieve of Eratosthenes or probabilistic prime
No, Python does not have a built-in function specifically for finding prime numbers. However, you can implement your own function using various algorithms.
No, a Prime number must be a positive integer greater than 1 that has no positive divisors other than 1 and itself. A negative number cannot be considered a prime number.

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