Re: Pell's Equation

On Mar 16, 9:51 am, Bruce Stephens <bruce+use...@xxxxxxxxxxxxxxxxxxxx>
wrote:
Richard Herring <junk@[127.0.0.1]> writes:
In message
<7a53bec3-bf3e-449f-9ad3-e88dae98c...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
austin.oby...@xxxxxxxxxxx writes

Austin, meet James.
James, meet Austin.

By way of explanation, the common home computer has 32- bit
architecture => the largest positive integer number it can handle is
2**31 = 2147483648

Didn't they teach the pen and paper methods for adding and subtracting
multi-digit numbers at your primary school?

Yes indeed!  He even includes that kind of thing in his email, which
conjures the rather wonderful image of teams of JSH supporters
furiously breaking RSA keys on paper.

It perhaps seems odd that he doesn't connect the obviously mechanical
nature of calculating things on paper with things that a computer
might do, but it fits with his other misunderstandings: at a deep
level, he fails to get it.

Hi

It perhaps seems odd that he doesn't connect the obviously mechanical
nature of calculating things on paper with things that a computer
might do, but it fits with his other misunderstandings: at a deep
level, he fails to get it.

I Sincerely hope I never get it - I mean your level of thinking.

You had me baffled for a moment as I tried to figure out whether you
are ahead of the pack or behind - I thought you were coming up with an
advanced piece of numerical analysis that I haven't yet heard of but
no you are not using worthwhile methods to factorise large numbers
that are too large to store in a computer. This is so primitive it
beggars belief. What you refer to as arithmetical method is like
trying to cut down a tree using a blunt stone. It may have been
taught in Fred Flinstone's primary school but certainly not in mine.
You even try to be secretive about it in case I might learn some thing
- What a hope .

For long hand (pen and paper) factoring of numbers of several hundred
digits a la RSA public-key you will need 1) an algorthm for finding
prime numbers, 2) an algorithm for finding square roots, 3 ) an
algorithm for finding prime factors and several million years in which
to do it.


The industry is on the look out for advanced algorithms that will make
it possible to do this in an acceptably short time and that may happen
some time when we are all least expecting it.

The industry is also looking to computer science to come up with a
means of storing these huge numbers that will enable the algorithm to
be programmed for automated running and thus reduced the time taken to
say minutes or even seconds.

I don't think they will be using your methods however, that
methodology pre-dates the well known school level algorithms that were
being taught in my primary school centuries back.

A thought - graphical methods of factoring giant numbers that use
GPS. This is something I am working on at present - might be too much
for you perhaps - adacrypt
.