I once boiled some potatoes of average size, by inserting a fork into them I thought they were boiled properly but cutting them in half, I saw the center is still raw with a lighter color. So how should I know it's enough boiling?
You would probably do best to check the internal temperatures of each and every potato. You can do this with a meat thermometer.
Potatoes are done if tender when pierced with a fork and the internal temperature reaches 210 degrees F. Use a meat thermometer to test for doneness.
(That's 98.8889 degrees Celsius, because I can't read Farenheit.)
Now, baking and boiling are different, and what you are going to end up doing with it or what type of potato you used will have an effect on this. However, you get the general idea. Thermometers will provide the best accuracy for any method of cooking.
If you want to really keep things accurate, you can use the ChefSteps method of selecting potatoes to begin with: http://www.chefsteps.com/activities/finding-perfect-french-fry-potatoes
So all your potatoes have about the same water content.
Then you can cut them all to exactly the same size.
Then you can put them in an immersion circulator/waterbath at 194°F / 90°C, use a special sous-vide bag thermometer to test the internal temperature (it pierces the bag and reseals it on the way out,) and you have the most accurate potatoes ever.
Mmmm, accurate potatoes.
A couple of ways:
Physical Resistance Test
Stick a knife in the potato and if you feel any resistance going in or coming out, it's not boiled thoroughly.
Physical Slide Test
Pick one up on a fork and if it can't stay on the fork at all they're done.
Visual Inner Test
Take one of out the boiling water, slice it in half, and see if it's done.
On how long to boil potatoes there probably really isn't any hard and fast, one-size-fits-all rule, (rule of thumb), primarily because the very word potato does not mean one and only one thing. There are many different varieties of potato. But potato density varies by type. So generally does potato size. Both of these factors play a crucial role in how much boiling time is required. (Well, maybe not crucial, but at least unavoidable.)
So very much of success in the kitchen relies on sheer consistency. (That, and actually remembering what does or doesn't work, because without that consistency is impossible.) But with potatoes, since there are really so many kinds, this is inherently challenging. Deliberate effort has to be made to be deliberate. Obviously that's a style to which not everyone is accustomed. I make no apology for that. But if one is willing to catalog one's work, mentally or otherwise, one can guarantee outcomes.
These things said, for any particular variety of potato, (and that's the key), always purchase and prepare potatoes of the same size. Yes, of course, the same size as each other. But that's not all I mean. The same size as the ones you last prepared, and before that, and so on. And equally importantly, the same amount. Use the scales if need be. For example, eight red potatoes the size of a biscuit may fit nicely into a particular pot you own. Or six russets. But if this is what you settle on, never go with russets the size of the reds or reds the size of the russets, and so forth. Yes, at a glance this may seem impractical or unduly laborious, but it's not. For example, to cook for a larger group you simply think in terms of multiples of what you normally do, cooking two or more batches instead of just one.
Add to this methodology. Some people start with cold water, some warm, some even boiling. Some people halve the potatoes, while some quarter them, et cetera. Whatever it is that you do, (for whatever reasons you do it), just make sure you always do just that. But always measure out the same amount of water. To state it in a single phrase: if materials do not vary and methods do not vary, outcomes will not vary.
Only in these ways can you arrive at specific knowledge of how much time it takes and, that is, be able to set a timer to it with absolute confidence. Same variety. Same size. Same amount. Same methodology. And the beauty of it is, you get to pick them all.