What is a Prime Number?

Put simply a prime number is a prime number that cannot be divided evenly into by any number other than itself and one. To me, in such simple terms, I sometimes can't understand why it is such a hot topic in mathematics today, but then I try to find a quick way to find million plus digit prime numbers and I understand. The problem with prime numbers is not that we can't find if 5364329 is prime or not, that is quite easy actually and would take less than a second, it is the method that we use. The obvious method would be to divide 5364329 by every number before it, and see if any go into it evenly. Or if we want to make it faster we can eliminate all the even numbers, since 5364329 is odd. Again to increase the efficiency we can only use numbers that are less than x =since any number greater than this x would have to be multiplied by a number less than x. For even greater efficiency, we can use only prime numbers < x, since 5364329 will be divisible by one of these prime numbers, if it is divisible by anything. But when we start dealing with number the size of 25364329 - 1, this method of trial division becomes grossly inefficient, especially since we don't have, at our disposal, all the prime numbers less then the square root of this rather large number. Move to So what's the problem? On a side note, I figure that since you are here, you must be at least slightly interested in prime numbers, so I challenge you to discover whether or not 5364329 is prime, tell me how long it took you, how you did it, and the factors (if it isn't prime).

 

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