How do you find out if a number is a prime number?

Answer 1

If it can not be divided by anything as a whole.

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The above is true, but "primeness" testing has become a major research branch of theoretical math. If I give you a large number, (eg: 123,456,789,012,345 ) can you prove it is or is not prime??

If you figure out a way, apart from attempting to divide it by all its potential factors like 2, 3, 4, 5, etc, etc. be sure to write it up and have it notarized, certificated, recorded, and then publish it. You will be the hero (or heroine) of the mathematical world. Also some of the eminent mathematical theoreticians will probably want to kill you.

Answer 2

Figure out all of the factors of that number. If the only factors are 1 and itself, then its prime. If its not just one and itself, its composite.