> While reading Simon Singh's book, "Fermat's Last Theorem", I got
> the urge to try and code some of the ideas in Forth. Hopefully
> somebody will find it amusing.

  ...

> The program can be found on ttp://www.iaehv.nl/users/mhx/programs.html

> -marcel

> > While reading Simon Singh's book, "Fermat's Last Theorem", I got
> > the urge to try and code some of the ideas in Forth. Hopefully
> > somebody will find it amusing.

> Unfortunately, Mr. Singh was not completely accurate in his description
> of Perfect Numbers (or maybe I didn't read the text carefully enough).

> In my program I used that Euclid found that perfect numbers are always
> a multiple of two numbers n1 and n2, n1 a power of two, n2 the next power
> of 2 minus 1:

>       6 = 2^1 * (2^2 - 1)
>      28 = 2^2 * (2^3 - 1)
>     496 = 2^4 * (2^5 - 1)
>   8,128 = 2^6 * (2^7 - 1)

> What the book didn't say is that in addition Euclid found that when n2
> is prime, n automatically is a perfect number. This opens the door to
> finding much larger Perfect Numbers, because [probability] algorithms
> exist that can test if a number is prime.

> I've written a Forth program that will check that, e.g., 2^3217 - 1 is
> prime and prints out the accompanying Perfect Number. For the given number
> the check takes only a few seconds on a P54C-166. (I can't show these
numbers
> as my news reader thinks I'm trying to post a binary in a non-binary
group).

> The program can be found on http://www.iaehv.nl/users/mhx/programs.html .

> -marcel

>> I've written a Forth program that will check that, e.g., 2^3217 - 1 is
>> prime and prints out the accompanying Perfect Number. For the given number
>> the check takes only a few seconds on a P54C-166. (I can't show these
>numbers
>> as my news reader thinks I'm trying to post a binary in a non-binary
>group).

> These prime numbers are called Mersenne's prime take a look at
> http://www.mersenne.org/prime.htm

>> I've written a Forth program that will check that, e.g., 2^3217 - 1 is
>> prime and prints out the accompanying Perfect Number. For the given number
>> the check takes only a few seconds on a P54C-166. (I can't show these numbers
>> as my news reader thinks I'm trying to post a binary in a non-binary group).
> When your newsreader thinks that this number is binary even if it is
> composed of ASCII characters, then it must really be a PERFECT number.
> :-)))

> > These prime numbers are called Mersenne's prime take a look at
> > http://www.mersenne.org/prime.htm

> Thanks. Both the original posting and the program sources mention
> this and, of course, use a table of Mersenne Primes. The point of
> the Perfect Number play is just to exercise the bignumber package
> I wrote 10 years ago (under direction of Albert van der Horst), and
> test the RABIN? procedure (It had a bug, but at least I had no
> problem at all reading the code :-)

> -marcel