Is It Prime?

A prime number is an integer number greater than one that cannot be divided evenly by any other numbers than one and itself. If a number can be divided evenly by any other numbers that one and itself, it is not a prime number.

Five (5), for example, is a prime number because there are no other numbers besides one (1) and five (5) that you can divide into five (5) evenly. Seven (7) is prime number for the same reason.

Eight (8) is not a prime number because it is evenly divisible by two (2) and four (4) as well as one (1) and itself (8). Twelve (12) is another example of a number that is not a prime number.

Let’s list the prime number from the first 25 of the integers; that is, let’s list the prime numbers from the number set 1 through 25. From this set, the prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, and 23. Note that 1 is not in the list of prime numbers because it is not a prime number by reason of the basic definition of a prime number (a prime number must be greater than one).

There are a couple of rules that we can use to identify those (integer) numbers that are not prime numbers. Rule #1: any number ending in the even numbers 2, 4, 6, and 8 are not prime number because they would all be evenly divisible by 2. Rule #2: any number ending in a 0 or 5 is not a prime number because it is evenly divisible by 5. Other than these two rules, it is difficult to generalize rules that eliminate numbers as prime numbers.

Why do we care about prime numbers? Well, they are useful in certain types of mathematical manipulations such as simplifying fractions by a process known as Prime Factorization (which we discuss elsewhere in this blog).

OK. We’ve listed the prime numbers from the set of the first 25 integers; that is, from the set of numbers 1 through 25. Can you list the prime numbers from the list of the first 100 integers; that is, from the set of integers 1 through 100? Give it a try. Then check your answer against the correct one by Clicking Here.

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