**Article Summary:** "Prime numbers are ordinary counting integers that can be
divided only by 1 and the prime number itself. What's so special about that?
Read a little information about prime numbers first and then learn how spies,
secret agents and super-large computers use prime numbers!"

Prime numbers are ordinary counting integers that can be divided only by 1 and the prime number itself. What's so special about that? Read a little information about prime numbers first and then learn how spies, secret agents and super-large computers use prime numbers! Let's think about the ordinary integers, like 1, 2, 96 and 643, for a minute and how you use them. The first thing that comes to mind is that you use integers every day as a tool for counting things and you know how to add, subtract, multiply and divide two integers at a time. That's easy so let's go a little further with relationships between integers. By now you should already know that: - The least common multiple (LCM) of two integers is the smallest positive integer that is a multiple of both. Example: LCM of 2 and 3 is 6.
- The greatest common divisor (GCD) of two integers is the largest positive integer dividing both. Example: GCD of 12 and 15 is 3.
Mathematicians are fascinated by the relationships between integers like LCM and GCD where numbers are related by division and multiplication. But some integers, even small integers like 11 and 17, just aren't related to any other numbers by multiplication and division. Integers like 11 and 17 can be divided only by 1 and the number itself. Any integer that can be divided only by 1 and itself is called a prime number. We already said that 11 and 17 are examples of prime numbers. Can you come up with all the prime numbers less than 50? If you think about prime numbers for a minute, you will realize that all prime numbers except for the integer 2 are odd numbers. That's because, of course, that all the even numbers greater than 2 can be divided by 2! In fact, 2 is the smallest prime number. Scholars know that centuries ago the ancient Egyptians and Greeks knew about prime numbers and in early times the number 1 was also considered to be a prime. However, modern mathematicians no longer call 1 a prime number. A popular test question is "What is the smallest prime number?" Remember, the correct answer is 2.
What is the largest prime? Since integers are infinite, we don't know. All the large primes that have been found since 1950 have been calculated using sophisticated computers, super-computers that are more complex than your PC. What about the spy games then? Prime numbers and computers have been linked since the 1950's. Do you recall learning about the Cold War between the United States and Russia in the 1960's? The U.S. CIA and Russian KGB both tried to keep the other from learning defense secrets about missile and rocket developments and other military secrets. Prime numbers played an important part in the secret spy codes that both countries used in relaying messages. In fact, prime numbers are still used in secret codes today. Hackers and other computer pirates try to steal information or break into private transactions. Computer security experts use extremely large prime numbers when they devise codes for protecting vital information that is transmitted between computers. That's not all. The mathematicians who studied prime numbers hundreds of years ago used the knowledge from primes to develop new areas of mathematics, like number theory and knot theory, which developers use today. While you might not use prime numbers directly yourself, they are a key part of modern mathematics and have important uses in the era of computers. Prime numbers less than 50: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 |