What is the first six-digit prime number?

A prime number is, by definition, a number that only has two factors: 1 and itself. If you find a number that isn't divisible by 3, 6, 9, and 7, that has nothing to do with whether it is prime or not. Consider 25. As you probably know, 5*5 = 25, so it is definitely a composite number. But, by your logic, it is prime. Do you see the problem here? I hope you aren't giving out answers like this to other questions.

........hehehe, I hope you didn't think my method was limited to that. What kind of fool do you take me for? =P

I was just giving a quick method that often eliminates the possibility that 3 and 9 would go into it, instead of having to divide the number by both of them (given that you don't have a calculator, this method is quicker). You should know whether a number is divisible by 5 (and 10) just by looking at it, so divide it by 7 and if that won't go evenly then you just eliminated all of the single digit numbers, which often helps a whole lot (considering most numbers are divisible by them, due to them being so small). ^___^

Thanks to: http://www.math.com/students/calculators/source/prime-number.htm

Hmm, interesting to know. Lol, I didn't really take into account two digit numbers in my method. Haha, my bad. ^_^

100001 is first prime number

Well, no, it isn't.