What is a Prime Number?

By Kardi Teknomo, PhD.

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Prime number has been fascinating for many great scientists and mathematicians for many centuries. Some people think that prime number contains some magic or mystics because of its irregularities and uniqueness.

Prime number is a positive integer number greater than 1 that divisible only by that number itself and one. For example 2, 3, 5, 7, 11, 13, 17, 19 are the first eight prime numbers. For technical reason, one is not called a prime number.

Example:

• 4 is not prime because 4 is divisible by 2
• 5 is prime because the only factors are 5 and 1
• 9 is not prime because 9 is divisible by 3

There are infinitely many prime numbers. Knowing about prime number, we can now divide any positive integer greater than 1 as either prime or not prime (also called composite number). A composite number has many divisors between 1 and that number, while prime number has no other divisor except 1 and that number.

Example:

• 24 is a composite number because between 1 and 24, we have 2, 3, 4, 6, 8 and 12 as divisors
• 11 is a prime number because there is no divisor between 1 and 11

Now I would like to ask:

• Is 97 prime?
• Is 94121 prime?
• Is 52127 prime?
• Is 52129 prime?

Below is an online interactive program that can help you to determine whether a positive integer is a prime or not. (Note: when your number is larger than 12 digits, you may have to wait to get the answer). Try to answer the following questions using this tool:

• If you make a number based on concatenation digits of primes, say 2, 23, 2357, 23571113171923, will they always becomes prime?
• Is 10585 prime?
• Can you delete or add one digit to the existing number and still produce prime?

In the next section, you will learn and have more fun on how to test whether a number is a prime number or a composite number using an algorithm called Sieve of Erastosthenes.

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This tutorial is copyrighted.

Preferable reference for this tutorial is

Teknomo, Kardi (2010) Prime factor tutorial. http:\\people.revoledu.com\kardi\ tutorial\BasicMath\Prime\