Conditional tests in primality by trial division

Question

My question is about the conditional test in trial division. There seems to be some debate on what conditional test to employ. Let\'s look at the code for this from Roset

Answer 1

sqrt(n) is accurate enough as long as your sqrt is monotone increasing, it gets perfect squares right, and every unsigned int can be represented exactly as a double. All three of these are the case on every platform I know of.

You can get around these issues (if you consider them to be issues) by implementing a function unsigned int sqrti(unsigned int n) that returns the floor of the square root of an unsigned int using Newton's method. (This is an interesting exercise if you've never done it before!)