python code trying to find prime number. Code is counting not prime number. Can't find why

Question

I am trying to find every prime number in a user chosen range, list them and count them. my code counts and list number that are not prime. I really can't find why? Could somebody please help me.

print("This code will count how many prime number exist in a certain range")
count = 0
lower = int(input("Enter lower range: "))
upper = int(input("Enter upper range: "))
prime = []
for num in range(lower, upper + 1):
    if num > 1:
        for i in range(2,num):
            if (num % i) == 0:
                break
            else:
                prime.append(num)
                break
print(prime)
print("There are", len(prime), "prime number between", lower, "and", upper)

Answer 1

Your primes part is wrong. I'm going to abstract that to a different method to make it easier. To be prime, a n%x must hold up for any x such that x is in the set of numbers [2,ceil(sqrt(n))].

Make sure you import math

def is_prime(num):
    for i in range(2, math.ceil(num**(1/2))):
        if num%i==0:
            return False
    return True

Then, just replace

if num > 1:
    for i in range(2,num):
        if (num % i) == 0:
            break
        else:
            prime.append(num)
            break

With,

if num>1:
   if is_prime(num):
      prime.append(num)

Answer 2

Your problem is that you dont wait all division checks to append the number to primes list:

            if (num % i) == 0:
                break
            else:
                prime.append(num)
                break

The fix for your code:

        is_prime =True
        for i in range(2,num):
            if num % i == 0:
                is_prime = False
                break

        if is_prime:
            prime.append(num)

---

$ python prime_test.py 
This code will count how many prime number exist in a certain range
Enter lower range: 12
Enter upper range: 20
[13, 17, 19]
('There are', 3, 'prime number between', 12, 'and', 20)

Answer 3

The problem is here,

    for i in range(2,num):
        if (num % i) == 0:    #If num is divisible by SOME i, it is not prime. Correct.
            break
        else:                 #If num is not divisible by SOME i, it is not prime. WRONG.
            prime.append(num)
            break

You should have checked the condition like this : If num is not divisible by ANY i, it is prime.

With minimum changes using else with for,

    for i in range(2,num):
        if (num % i) == 0:
            break
    else:
        prime.append(num)

---

Read more : Why does python use 'else' after for and while loops?

Answer 4

Here is a solution to get the prime number form a list. Ask user for range between the prime number should be created and store it in list:

list4=list(range(3,10,1))  
prime_num=[x for x in list4 if x%2!=0 and x%3!=0]