What is the output of this condition in the Prime Function?

问题

I found this code from another post and I'm trying to understand a part of this solution.

function sumPrimes(n) {
  function isPrime(num) {
    for ( var i = 2; i < num; i++ ) {
        if ( num % i === 0 ) {
            return false;
        }
    }
    return true;
}
    var arr = 2;
    for ( var i = 3; i <= n; i+=2 ) {
        if ( isPrime(i) ) {
            arr += i;
        }
    }
return arr;
}
console.log(sumPrimes(10));

The part I'm asking about is this particular function

function isPrime(num) {
        for ( var i = 2; i < num; i++ ) {
            if ( num % i === 0 ) {
                return false;
            }
        }
        return true;
    }

especially this line in question

num % i === 0

What I can understand is that arr is an array that product every odd number after 2 (for example, [2, 3, 5, 7, 9, 11, 13, 15, 17]). Then every number is run through function isPrime. What I'm trying to understand is what are the outputs of num % i === 0 in relation to for ( var i = 2; i < num; i++ )?

Are the outputs like this?

3(num) % 2(i)
5(num) % 3(i)
7(num) % 4(i)
9(num) % 5(i)
11(num)% 6(i)

回答1:

for ( var i = 2; i < num; i++ ) {
    console.log(`${num} % ${i} === ${num % i}`); // Extra line
    if ( num % i === 0 ) {
        return false;
    }
}

In this code, what the code is actually doing is it's going through every single number between 2 and num, assigning it to the variable i, and checking if num is divisible by i. If it is, then it'll return false.

The % function (called the modulo function), basically takes two numbers, and returns the first number's remainder when divided by the second number. So, for example:

5 % 2 // = 1, 5/2 = 2 with 1 left over
7 % 3 // = 1, 7/3 = 2 with 1 left over

If the remainder is 0, then obviously the first number is divisible by the second number, since there's nothing left over. So the line num % i === 0 is checking for divisibility, essentially - it's checking if num is divisible by i.

For example, when checking 5 (with the extra console.log line), this is what's outputted to the console:

5 % 2 === 1
5 % 3 === 2
5 % 4 === 1

And this is what's outputted with 6 as num:

6 % 2 === 0

(It's stopped, because false is returned.)

回答2:

The % operator is the modulus operator. It returns the remainder after division. So n % x will be zero any time n is evenly divisible by x. In this example it's testing whether the number is divisible by any of the previous numbers.

The line num % i === 0 returns true whenever num is evenly divisible by i

回答3:

It means that if the rest of division of num by i equal 0 then num is divided by a number other than 1 and itself, then it is not a prime nubmer so return false. ('%' mean modulo or rest of division)

回答4:

% is the modulus operator. x%y = x mod y = the remainder when x is divided by y. So 4%1=0, 4%3=1, and 4%4=0.

Therefore, x%y==0 is equivalent to "x is divisible by y". Therefore the loop is checking, for each number from 2 to num - 1, is num divisible by that number. For a prime number, the answer will always be no. So any case where num is divisible by i, it is definitely not prime. If num is not divisible by any number in the range, then it's prime.

Interesting side note: the loop doesn't have to go all the way to num-1 - it could stop at sqrt(num) (rounded), do you see why?

来源：https://stackoverflow.com/questions/45383561/what-is-the-output-of-this-condition-in-the-prime-function

标签

javascript

function

primes