In mathematical speak, a prime number is defined as a positive integer that can only be divided evenly by itself or 1. For example, 2 can be classified as such a number because 2 divided by 2 is 1, and 2 divided by 1 is 2. Likewise, 3 is also a prime number. However, 4 is not, and here’s why: This number can be divided evenly by itself and 1; just like prime numbers, but it can also be divided evenly by 2 . The same will apply to the number 6, which can be evenly divided by 2 and 3. The number 8 can be divided evenly by 2 and 4, so it too does not qualify as a prime number. Because the preceding numbers of 4, 6, and 8, can be divided evenly by more than just itself or 1, they are known as composite numbers.

You may have noticed a bit of a pattern here. With the exception of 2, even numbers will never be prime numbers. To illustrate, take a look at 10, 12, and 14. In addition to being divisible by 1 and itself, 10 can also be divided evenly by 2 and 5. The number 12 can be divided by 2, 3, 4, and 6. The number 14 can be divided by 2 and 7. Thus, every even number except 2 is a composite number. So does this mean that every odd number is a prime number?

No, it does not. While every prime number except 2 will indeed be an odd number, not all odd number are prime. Let’s look at the number 9. Can this be divided evenly by more than just 1 or itself ? Yes, it can. It is also evenly divisible by 3, so 9 is not a prime number. Conversely, 5 and 7 are prime numbers. Likewise, 11 and 13 are prime numbers, but 15 is not. Does this make sense?

This goes on for infinity, really. The larger the prime number, the bigger the gap will be between its nearest neighbors. At this writing, the largest prime number that has been calculated contains 12,878,189 digits! Many people; especially those not fond of math in the first place, will question why anyone would bother or care to know whether or not a number is classified into this category. The simplest answer to this is that prime numbers serve as the building blocks to all positive integers; just as something such as DNA functions as our building blocks. In other words, everything has a purpose; a rhyme and reason as to how and why it is formed. A sequence of events; however logical or illogical it may appear, is necessary for something to exist.

As for finding prime numbers, a simple calculator will suffice for the small ones. However, when locating the huge ones, such as those with millions of digits, complex computer programs and equations must be utilized.

http://primes.utm.edu/largest.html#intro

http://www.mathsisfun.com/definitions/prime-number.html