Python-使用除数检查数字是否为质数

Question

I have to write a program that checks if a number is a prime number by going through divisors in the range(1,num). (For ex. if the input is 5, the program will check if 2 is a divisor, then 3, then 4). Can someone explain how I can put the last expression in my program (the "this is a prime number" print function), so that it appears only after the "else" function in the "for" loop and not the "if div == 0:" statements? Thank you!

while True:
    num = int(input("Enter a positive number to see if it's a prime number: "))
    if num > 1:
        break
    elif num == 1:
        print("1 is technically not a prime number.")
    else:
        print("Number cannot be negative- try again.")

for num1 in range(2,num):
    div = num%num1
    if div == 0:
        print(num1,"is a divisor of",num,"... stopping.")
        print(num,"is not a prime number.")
        break
    else:
        print(num1,"is NOT a divisor of",num,"... continuing")

print(num,"is a prime number!")

Answer 1

There are many ways to do this:

Set a flag!

is_prime = True # a boolean flag
for num1 in range(2,num):
    div = num%num1
    if div == 0:
        print(num1,"is a divisor of",num,"... stopping.")
        print(num,"is not a prime number.")
        is_prime = False
        break
    else:
        print(num1,"is NOT a divisor of",num,"... continuing")

 if is_prime:
     print(num,"is a prime number!")

Use for-else !

for num1 in range(2,num):
    div = num%num1
    if div == 0:
        print(num1,"is a divisor of",num,"... stopping.")
        print(num,"is not a prime number.")
        is_prime = False
        break
    else:
        print(num1,"is NOT a divisor of",num,"... continuing")
 else: 
      print(num,"is a prime number!") # will execute only when for-loop ends

Answer 2

Python's for expression has an optional else clause :

Loop statements may have an else clause; it is executed when the loop terminates through exhaustion of the list (with for) or when the condition becomes false (with while), but not when the loop is terminated by a break statement.

So your code should look like this:

while True:
    num = int(input("Enter a positive number to see if it's a prime number: "))
    if num > 1:
        break
    elif num == 1:
        print("1 is technically not a prime number.")
    else:
        print("Number cannot be negative- try again.")

for num1 in range(2,num):
    div = num%num1
    if div == 0:
        print(num1,"is a divisor of",num,"... stopping.")
        print(num,"is not a prime number.")
        break
    else:
        print(num1,"is NOT a divisor of",num,"... continuing")
else:
    print(num,"is a prime number!")

Answer 3

Given that you have already covered a division by 1, all you have to do is count if there is only one more divisor (the number itself). So to keep your code structure I added a counter.

while True:
    num = int(input("Enter a positive number to see if it's a prime number: "))
    if num > 1:
        break
    elif num == 1:
        print("1 is technically not a prime number.")
    else:
        print("Number cannot be negative- try again.")

for num1 in range(2,num):
    div = num%num1
    count = 0
    if div == 0:
        print(num1,"is a divisor of",num,"... stopping.")
        print(num,"is not a prime number.")
        break
    else:
        count += 1
        print(num1,"is NOT a divisor of",num,"... continuing")

if count == 1:
    print(num,"is a prime number!")

Answer 4

I added one line sys.exit()

while True:
num = int(input("Enter a positive number to see if it's a prime number: "))
if num > 1:
    break
elif num == 1:
    print("1 is technically not a prime number.")
else:
    print("Number cannot be negative- try again.")

for num1 in range(2,num):
div = num%num1
if div == 0:
    print(num1,"is a divisor of",num,"... stopping.")
    print(num,"is not a prime number.")
    sys.exit()
else:
    print(num1,"is NOT a divisor of",num,"... continuing")

print(num,"is a prime number!")