Print prime numbers in a range in Python

This program prints every prime number between a start and an end value. It reuses the is_prime() function from the prime number check page.

The program

import math


def is_prime(n):
    if n < 2:
        return False
    for i in range(2, math.isqrt(n) + 1):
        if n % i == 0:
            return False
    return True


start = int(input("Start: "))
end = int(input("End: "))

primes = [n for n in range(start, end + 1) if is_prime(n)]

print(f"Primes from {start} to {end}:", *primes)
print("Count:", len(primes))

Typed in this example: 10, 50. Press Run to type your own.

Start: 10
End: 50
Primes from 10 to 50: 11 13 17 19 23 29 31 37 41 43 47
Count: 11

How it works

• range(start, end + 1) includes the end value, so 50 is checked too.
• The list comprehension [n for n in ... if is_prime(n)] keeps only the numbers for which is_prime(n) returns True.
• A start value below 2 is not a problem: is_prime() returns False for 0, 1 and negative numbers.

Another way: the Sieve of Eratosthenes

To find all primes up to a limit, the Sieve of Eratosthenes is much faster than testing each number. It starts by marking every number as possibly prime. Then, for each prime it finds, it crosses out all multiples of that prime.

limit = 50

is_prime = [True] * (limit + 1)
is_prime[0] = is_prime[1] = False

for n in range(2, int(limit ** 0.5) + 1):
    if is_prime[n]:
        for multiple in range(n * n, limit + 1, n):
            is_prime[multiple] = False

primes = [n for n in range(limit + 1) if is_prime[n]]
print(*primes)

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47

• is_prime[n] is True while the number n has not been crossed out.
• Crossing out starts at n * n, because the smaller multiples (like 2 × 5 when n is 5) were already crossed out by a smaller prime.
• range(n * n, limit + 1, n) counts up in steps of n, so it gives exactly the multiples of n.