Prime numbers between given two numbers in Julia and Python comparison

Question

See the Python code for finding prime numbers between given two numbers lower and upper:

lower = 3
upper = 15

print("Prime numbers between", lower, "and", upper, "are:")

for num in range(lower, upper + 1):

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

Python Output:

Prime numbers between 3 and 15 are:
3
5
7
11
13

Almost similar code in Julia gives incorrect output. See the Julia code below:

lower = 3
upper = 15
println("Prime numbers between ", lower, " and “, upper, " are:”)
for num in lower:upper    
    for i in 2: num-1
        if (num % i) == 0
            break           
        else
            println(num)
            break
        end
    end
end

Julia Output:

Prime numbers between 3 and 15 are:
3
5
7
9
11
13
15

Clearly, 9 and 15 are not primes. Why does Python code gives correct output and Julia code does not. Any way to fix it using the same algorithmic logic?

Answer 1

Here is the code I would use that keeps the same algorithmic logic per your request (I write this code this way as the condition inside the loop is not only efficient but also reads naturally: "either any of the numbers from the range 2:num-1 divides num or print num"):

julia> lower = 3
3

julia> upper = 15
15

julia> println("Prime numbers between $lower and $upper are:")
Prime numbers between 3 and 15 are:

julia> for num in lower:upper
           any(i -> num % i == 0, 2:num-1) || println(num)
       end
3
5
7
11
13

Per comments to your question in Julia you do not have else clause in for loop. However using the any function keeps the same logic as your code as it is a short-circuting function (achieving the same effect as break in your for loop).

If anything is not clear in my code please let me know.

---

EDIT:

I will rewrite the code to explain how it works.

First the || part. It uses the short-circuting behavior of || operator. So on the first level this can be rewritten as:

julia> lower = 3
3

julia> upper = 15
15

julia> println("Prime numbers between $lower and $upper are:")
Prime numbers between 3 and 15 are:

julia> for num in lower:upper
           iscomposite = any(i -> num % i == 0, 2:num-1)
           if !iscomposite
               println(num)
           end
       end
3
5
7
11
13

Now, as commented any is doing short circuting also so it is equivalent to writing:

julia> lower = 3
3

julia> upper = 15
15

julia> println("Prime numbers between $lower and $upper are:")
Prime numbers between 3 and 15 are:

julia> for num in lower:upper
           iscomposite = false
           for i in 2:num-1
               if num % i == 0
                   iscomposite = true
                   break
               end
           end
           if !iscomposite
               println(num)
           end
       end
3
5
7
11
13

Answer 2

Your Julia code seems to print inside and break the factor checking loop instead of waiting for all factors to be verified. (I don't know Julia but that seems to be an obvious difference).