Associated Topics || Dr. Math Home || Search Dr. Math

### Irrational and Prime Numbers

```
Date: 4/1/96 at 7:14:46
From: Leigh Ausband
Subject: Pi

A question from Mrs. Fields' seventh grade math classes at Robert
Smalls Middle School, Beaufort, SC.

Please explain the concept of irrational numbers. Also, do you
think there is a highest prime number?

Sincerely,
Tiffanne' Mahomes
```

```
Hi Tiffanne'

Mathematicians have proven that prime numbers are infinite -
so no, there isn't a highest prime number.  However, there IS
a 'largest known prime' - the highest one we've found to date.
According to the sci.math FAQ, this is

(2 to the 859433rd power) -1.

Wow, that's big!

Irrational numbers are numbers that can't be expressed as a ratio
between two integers.

Some rational numbers:  1/3, 8, -295, -983

An example of an irrational number is the square root of 2.

As far as I know, the square root of two was the first known
irrational number.  Do you know the Pythagorean theorem?  At

http://mathforum.org/pow/solution15.html

there's a great picture of this theorem, which says that in a right
triangle, the square on the first short leg added to the square
on the second short leg equals the square on the hypotenuse.

Well, what happens if you have a right triangle with short sides
of 1 and 1? The hypotenuse winds up having a length of the
square root of two!

-Doctor Jodi,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Number Theory

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/dr.math/