Python Prime Number Generator Prints 4

Question

I have a school exercise where I have to make a Prime Number Generator and Optimize it later on. After I did some optimization my Generator started to also print the number "4" which is obviously not a prime number.

My Code looks like this:

import time
#Primzahlen errechnen
c = 0
print("Enter Upper Value:")
Max_wert = input()
x = int(Max_wert)

print("Prime Numbers between 0 and ", x, "are:")
time.sleep(1) # Pause für 2 Sekunden

for num in range(2, x):
    num2 = int(num / 2)
    for i in range(2, num2):
        if (num % i) <= 0:
            break
    else:   
        print(num)
        c+=1

print(c, "Prime Numbers were found")

When I remove the line: > num2 = int(num / 2) and change num2 in the for loop back to num then everything works fine.

Answer 1

The problem is that in the for loop you have to test from 2 to floor(sqrt(num)) not to num/2 (any further control is useless, check this out: Why do we check up to the square root of a prime number to determine if it is prime? ) and , most important, the range for i has to be between range(2, num2 + 1) and not range(2, num2)

The for loop code will be:

for num in range(2, x):
    num2 = math.floor(math.sqrt(num))
    for i in range(2, num2 + 1):
        if (num % i) <= 0:
            break
    else:   
        print(num)
        c+=1

An example output will be:

Enter Upper Value:
10
Prime Numbers between 0 and  10 are:
2
3
5
7
4 Prime Numbers were found

Answer 2

In the loop for i in range(2, num2): when num is between 2 and 5 program flow will not enter the for loop.

So they 2,3,4,5 are just getting printed, not because they are prime or not prime.

Because num2=int(num/2), when num is in [2,5], for loop range is (2,1)(2,1)(2,2)(2,2).

when num=2,3 range(2,1) doesn't make sense as you are asking it to start at 2 and go till 1, so it exits for loop and goes directly to else block printing 2 AND 3.

when num=4,5 range(2,2) will not give anything as ur asking it to start at 2 and go till 2(not inclusive) so again it goes directly to else block printing 4 and 5.

For values of num, more than 5 ur code runs as it should.

So ur for loop should be:

for num in range(2, x):
    num2 = int(num / 2 + 1)
    for i in range(2, num2):
        if (num % i) <= 0:
            break
    else:   
        print(num)
        c+=1