如何使用 python 检查素数

Question

I wrote the code below to check for prime numbers but when I run the code both the if and else statements execute the same output.

n = int(input("enter a number\n"))
for i in range(2, n):
    if n % i == 0:
        print(f"{n} is not prime")
    else:
        print(f"{n} is prime")

Answer 1

Sympy.isprime is probably the most efficient way unless you want to check various numbers. In that case, it's better to use the Sieve of Eratosthenes .

If you do not want to use modules or semi-complicated algorithms, the following plain code works perfectly if you need to check just a few numbers smaller than 10**6.

def isprime(num):
    for n in range(2,int(num**0.5)+1): 
        if num%n==0:
            return False
    return True

Answer 2

The issue you have is that your loop prints out something on every iteration. You can't do that if you only want to print that n is prime when you're sure it is. You can only be sure of that when your whole loop completes.

This is easiest in a function, where you can return whenever you have a firm answer:

def prime_check(n):
    for i in range(2, n):
        if n % i == 0:
            return False
    return True             # this only runs after the whole loop ends


n = int(input("enter a number\n"))
if prime_check(n):
    print(f"{n} is prime")
else:
    print(f"{n} is not prime")

If you want to keep the check inline, rather than using a function, you can do that too, with some clever use of break and the else clause attached to the loop , rather than the if . Such a clause only runs if the loop exits normally, not if it's exited early by a break statement. This can be a bit confusing, which is why I put it second, after the return version that is a lot more clear.

n = int(input("enter a number\n"))
for i in range(2, n):
    if n % i == 0:
        print(f"{n} is not prime")
        break
else:                       # the else is attached to the for loop now, not the if
    print(f"{n} is prime")  # this line is only runs if no break happened in the loop