Python Program to Print all Prime numbers in an Interval

Last Updated : 13 Aug, 2026

The task is to print all prime numbers within a given interval by taking a starting and ending number. A prime number is a number greater than 1 that has no divisors other than 1 and itself.

Example: In the range [2, 7], the prime numbers are 2, 3, 5, and 7. Different approaches can be used to find prime numbers in an interval.

Using sieve of Eratosthenes

Sieve of Eratosthenes finds all prime numbers up to a given limit by marking the multiples of each prime number as non-prime. It is efficient for finding multiple prime numbers within a large interval.

Python 
x, y = 2, 7

primes = [True] * (y + 1)
primes[0], primes[1] = False, False

for i in range(2, int(y ** 0.5) + 1):
    if primes[i]:
        for j in range(i * i, y + 1, i):
            primes[j] = False

result = [i for i in range(x, y + 1) if primes[i]]

print(result if result else "No")

Output
[2, 3, 5, 7]

Explanation:

  • primes creates a Boolean list where each index represents a number.
  • False is assigned to 0 and 1 because they are not prime.
  • The loop checks numbers up to √y.
  • Multiples of each prime are marked as False.
  • The remaining True values in the given interval represent prime numbers.

Using trial division

Trial Division checks each number in the interval for divisibility. Each number is tested from 2 to its square root.

Python 
x, y = 2, 7 
res = []

for n in range(x, y + 1):
    if n <= 1:
        continue 
    is_prime = True  # assume n is prime
    for i in range(2, int(n ** 0.5) + 1):
        if n % i == 0:
            is_prime = False  # n is not prime
            break
    if is_prime:
        res.append(n)  # add prime number
print(res if res else "No")

Output
[2, 3, 5, 7]

Explanation:

  • Each number from x to y is checked.
  • Numbers less than or equal to 1 are skipped.
  • Each remaining number is tested for divisibility up to √n.
  • If a divisor is found, the number is not prime.
  • Numbers with no divisors are added to result.

Using sympy library

SymPy provides the primerange() function to generate prime numbers within a specified range.

Python 
from sympy import primerange
x, y = 2, 7

primes = list(primerange(x, y + 1))
print(primes if primes else "No")

Output

[2, 3, 5, 7]

Explanation:

  • primerange(x, y + 1) generates prime numbers from x through y.
  • list() converts the generated values into a list.
  • The result is stored in primes.

Note: SymPy is an external Python library, not part of the standard Python installation, therefore it must be install first using command - "pip install sympy"

Using naive approach

The naive approach checks every number by testing divisibility from 2 to n // 2. It is less efficient than trial division and is mainly suitable for small intervals.

Python 
x, y = 2, 7 
res = []  

for i in range(x, y + 1):
    if i <= 1:
        continue  
    for j in range(2, i // 2 + 1):
        if i % j == 0:
            break 
    else:
        res.append(i)  
print(res if res else "No")

Output
[2, 3, 5, 7]

Explanation:

  • Each number from x to y is checked.
  • Numbers less than or equal to 1 are skipped.
  • Each remaining number is divided by values from 2 to n // 2.
  • If a divisor is found, the loop stops.
  • If no divisor is found, the number is added to result.
Comment

Explore