Python program to print all Prime numbers in an Interval

Given two positive integers start and end. The task is to write a Python program to print all Prime numbers in an Interval.

Definition: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first few prime numbers are {2, 3, 5, 7, 11, ….}.

The idea to solve this problem is to iterate the val 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.

Below is the Python implementation:

Python3

# Python program to print all
# prime number in an interval

def prime(x, y):
    prime_list = []
    for i in range(x, y):
        if i == 0 or i == 1:
            continue
        else:
            for j in range(2, int(i/2)+1):
                if i % j == 0:
                    break
            else:
                prime_list.append(i)
    return prime_list

# Driver program
starting_range = 2
ending_range = 7
lst = prime(starting_range, ending_range)
if len(lst) == 0:
    print("There are no prime numbers in this range")
else:
    print("The prime numbers in this range are: ", lst)

Output: 

The prime numbers in this range are: [2,3,5]

Time Complexity: O(N²), where N is the size of the range.

Auxiliary Space: O(N), since N extra space has been taken.

Approach 2 : Sieve of Eratosthenes 

Python3

def sieve(x, y):
    # create a list of all the numbers in the range
    numbers = [i for i in range(x, y+1)]

    # start with the first number in the list
    i = 0

    # loop until we reach the end of the list
    while i < len(numbers):
        # if the current number is not already crossed out,
        # cross out all of its multiples
        if numbers[i] is not None:
            for j in range(i+numbers[i], len(numbers), numbers[i]):
                numbers[j] = None
        i += 1

    # return the list of prime numbers
    return [n for n in numbers if n is not None]

# Driver program
starting_range = 2
ending_range = 7
lst = sieve(starting_range, ending_range)
if len(lst) == 0:
    print("There are no prime numbers in this range")
else:
    print("The prime numbers in this range are: ", lst)

Output : 

The prime numbers in this range are: [2,3,5]

Time Complexity : O(nlogn)

Auxiliary Space : O(n)

The above solution can be optimized using the Sieve of Eratosthenes. Please see print prime numbers in a range for details.