Impossible Word

Date: 04/14/2001 at 10:08:51
From: Dustin Babler
Subject: Word Values 

What is a word that comes out to 575,151 when multiplying its letters' 
values together? 

For example, belch = 376,200 (25*22*15*24*19). 

I have come close, but not close enough!

Thank you for your help.
Dustin

Date: 04/16/2001 at 13:46:43
From: Doctor TWE
Subject: Re: Word Values 

Hi Dustin - thanks for writing to Dr. Math.

The first thing I did when I saw this problem was to find the prime 
factorization of 575151 because that would limit the possible letters 
I had to work with. What I found out was that 575151 = 3*191717, and 
191717 is a prime number. (I have a computer program that verified 
that for me.) 

Since there is no 191717th letter in our alphabet, the 
construction must be impossible!

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/