How to Find Prime Numbers in Python

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

• What is a Prime number?
• Python Program to check 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:

num = 13
if num > 1:
for i in range(2, num//2):
if (num % i) == 0:
print(num, "is not a prime number")
break
else:
print(num, "is a prime number")
else:
print(num, "is not a prime number")

Output: 13 is a prime number

Optimized Method

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.

Example:

def isPrime(n) :
if (n <= 1) :
return False
if (n <= 3) :
return True
if (n % 2 == 0 or n % 3 == 0) :
return False
i = 5
while(i * i <= n) :
if (n % i == 0 or n % (i + 2) == 0) :
return False
i = i + 6
return True
if (isPrime(11)) :
print(" true")
else :
print(" false")
if(isPrime(15)) :
print(" true")
else :
print(" false")

With this, we have come to the end of our article. I hope you understood how to write a prime number program in Python Programming.

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