Carel's pages on Mathematics and Freeware
The pages your are about to view is all about freeware I have written and my hobby namely Mathematics.

I live in South Africa Gauteng Pretoria and is maried to my wife Hanlie and we have three naughty boys Christoff, Dirk-Daniel and little Carel.

I am an engineer working for Telkom the national Telecoms service provider.

Currently I work in the DC electrical power section

In my spare time I work out brain teasers and Mathematical proofs.
The wife and me at the Octoberfest in Pretoria. I am a little bit tipsy as you can see
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Links:
Family Homepage with lots of shareware
personal Information
Name: Carel van der Westhuizen
Email: vdwestch@mweb.co.za

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The Fundamental Theorem of Arithmetic
The fundamental theorem of arithmetic (or unique-prime-factorization theorem) states that every
natural number greater than 1 can be written as a unique product of prime numbers.

Proof: Suppose it is not so, then there must be one such smallest number z>1
that cannot be written as the product of primes. So this number is not prime
because then it is the product of 1 and a prime. It is therefore
composite. So z = a.b , but then a and b are the product of primes because z
is the smallest number that cannot be written as the product of primes
and a and b are both smaller than z. But if both a and b are products
of primes then so must be z, because z = a.b This is a contradiction
so our assumption that z is not the product of primes must
be wrong

Download this Lotto generator for free

Download this nice and easy to use Picture viewer/Erazer for free use. Comments most welcome.
If the program does not work, it is most probabely because a VB DLL is missing.
If so, contact me and I will forward it to you.

Prime numbers are numbers only dividible by itself and 1. One is by definition not prime.
The first few primes are 2,3,5,7,11,13,17,19,23 and so on.

The number of prime numbers less than n is about n/ln(n). This is the great prime number theorem.

There is always at least one prime number between n and 2n

The list of prime numbers is infinite. Suppose it was not so. Then the list would be finite.
Now lets take the product of all these prime numbers in the list and call it z
Now form s = z+1. Then no prime in the list divides s
So s must be either prime or a product of primes not in the list
Therefore the list must be infinite

Two is the only even Prime number

Biggest Mersenne Prime found so far is (243112609) - 1 and it has 12 978 189 digits

Proth prime I discovered on 30/06/2006 is 49*(2501238) + 1
This prime has 150 890 digits
This prime is also a generalized Fermat as it divides 10^(2^501235) + 3^(2^501235)
Recently in 2008 I discovered a new prime 67*2^684258 + 1 with 205985 digits.

More Maths on Page 2

Learn something new, turn the Page

Go to Page 2 it contains more on Maths

Go to Page 3 it also contains more on Maths

Go to Page 4 it has alternative solutions to the Quadratic polynomial

Go to Page 5 it has an exact solution to the Cubic polynomial

Go to Page 6 it has an unique method to solving the Quartic

Go to Page 7 it has a nice proof on primes

Go to Page 8 it has a nice induction proof

Go to Page 9 it has some information regarding mersenne primes and the Lucas Lehmer test
It also contains a small applet demonstrating the test for primality

Go to my Fermat page it has a infinite descend proof using the method of Fermat

Go to my Goldbach page it shows the relationship of the prime pairs with
the great prime number theorem

Go to my page on the bridges of Konigsberg and see if you can solve the puzzle

Go to my page on the theorem of Pythagorus and see the beauty of his genius. Three Proofs

Go to my page on my book Paradox
and read what the book is all about
There is also a picture of the book and some examples of the puzzles



Go to my links and visit some nice sites