如何处理 Python 中素数检查的否定情况？

Question

With regard to the "xrange" function - ("range" in Python3) what happens when I do a negative check inside a loop? In this case, a negative number could be regarded as an edge case, but always returns None. Any insights?

Answer 1

The problem is you are checking if the number is negative inside the for loop. For instance if x=-3, then you are trying to run a for loop in range(2,-1) which is None. So the for loop never runs and hence returns True.

def isprime(x):
 if x<=0:
   return(False)
 for a in range(2,(x//2)+1):
   if(x%a==0):
     return(False)
 return(True)

Answer 2

By it's elementary school definition, prime numbers are defined for positive numbers only, thus your function should return False for every negative number, for example:

def isprime(x):
    if x <= 0:
        return False
    for a in range(2, (x//2)+1):
        if x % a == 0:
            return False
    return True

That being said, it is possible to extend the definition (as done in some fields in math), to include negative numbers as well (for further discussion see here and here ). In this case, for every negative number -n , -n is prime iff n is prime. Therefore your code could be something like:

def isprime(x):
    if x <= 0:   # or use any |abs| method you'd like, like numpy's
        x = -x
    for a in range(2, (x//2)+1):
        if x % a == 0:
            return False
    return True