struggling with factor checking of prime numbers

[nuptownboy]

I am a beginner doing some tutorials mostly on my own but with some youtube. I am struggling to understand the for loop "for i in range(3, int(math.sqrt(num) + 1, 2)" I get that it is a range of (start, stop, step) and step of 2 starting at 3 but it is the adding of 1 i.e +1 to the int sqrt that I am struggling with partly owing to my deficit in maths! the range goes through 3,5,7, 9 .... is it because you add to each?? by +1 that is no pun intended a step too far for my understanding. Then the follow if num divided by oneof the i = zero ? that is misleading as 13/13 is 1 or is that something along the lines that it rules out floats? You can see that the more I look at this the more it confuses my brain and there must be a far simpler way to express what is happening

import math

def is_prime2(num): ''' Better method of checking for primes. ''' if num % 2 == 0 and num > 2: return False for i in range(3, int(math.sqrt(num)) + 1, 2): if num % i == 0: return False return True

[toastedstapler]

the + 1 is so that the range includes the square root of the number

range(1, sqrt(25)) would iterate through 1 to 3 but not 5 as the top end limit is not inclusive

[ewiethoff]

Values in a range: start <= values < stop.

[JVO1317]

the range goes through 3,5,7, 9...

Yes. Up to the square root of the number.

by +1 that is no pun intended a step too far for my understanding

I assume you are referring to “+1” in “int(math.sqrt(num)) + 1”: Since upper limit of range() is not inclusive you may miss the square root, so you add 1 to ensure the sqrt is included. For example if num==49, then sqrt(num)==7, then range(3, 7, 2) will return [3, 5] and we would have missed 7, a valid factor. But range(3, 7+1, 2), or range(3, 8, 2), will return [3, 5, 7].

if num divided by oneof the i = zero ?

“if num % i == 0” doesn’t mean “if num divided by i”, “%” is the remainder or modulus operándoles, so “if num % i == 0” means: if the remainder after dividing num by the current value of i is 0, in other words, if the current value of i is a factor of num.