Bug & Performance improvement

You code is already really fast, which is awesome. Nevertheless you could improve the performance with some simple changes. No idea why nobody already suggested that.

Bug:

Your way to check if the given argument is a number is clever but does not catch all possible types of arguments. The following arguments are possible:

prime(-2)        == False
prime(1)         == False
prime(2)         == True
prime(1.5)       == True  <-- Wrong
prime(Infinity)  == False
prime(undefined) == False
prime(NaN)       == False
prime('a')       == False
prime("a")       == False
prime([])        == False
prime([2])       == True   <-- Wrong
prime([1,2])     == False

I suggest you to use Number.isInteger() to make sure the given argument is definitely an existing integer. It is supported by default by all browsers.

Performance:

• l.7: Instead of calculating the square of every possible divisor you could calculate the integer-square root just once, which may increase the runtime for small but should reduce the runtime for large numbers

for (var i = 5, j = Math.round(Math.sqrt(num)); i <= j; i += 6) {

• l.7/8: for every iteration you do 2 additions i + 2 and i + 6, even though i+2 and i+4 are sufficient, has a very small influence on performance and may already be done by the compiler

for (var i = 5, j = Math.round(Math.sqrt(num)); i <= j; i += 4) {
  if (num % i === 0) return false;
  i += 2;
  if (num % i === 0) return false;
}

Hope i can help.

Start at the prime-checking function and inspect the argument validation and divisor loop around lines 7-8. Confirm the behavior for the listed inputs, then ensure non-integers and non-numbers are rejected and the proposed divisor-loop changes preserve correct prime results and improve large-number performance.