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
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 1950s. Do you recall learning about the Cold War
between the United States and Russia in the 1960s? 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
While you might not use prime numbers directly yourself, they are
a key part of modern mathematics and have important uses in the era
Prime numbers less than 50: 2 3 5 7 11 13 17 19 23 29 31 37 41 43