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/