Re: A factoring algorithm

hart_wb@yahoo.com writes:
> Hi,
>
> I have a new factoring algorithm which seems to be very fast with
> certain kinds of numbers.
>
> For example it will factor numbers which are the product of two primes
> which are both of the "same kind", and fairly close together (say are
> the same length to within 3 or 4 digits -though that isn't an absolute
> requirement if you do some fiddling and have a little more time), where
> by "same kind" I mean that they are both of the form:
>
> a*b^n+c where a, b and c are "small"

Such as factoring

10000000000000000000000000000000000000121000000000000000000070000000000000000000000000000000000000847

?

You just need to find b, and then everything else drops out almost instantly.

> It's a wierd class of numbers to factor, but the algorithm is not
> contrived.
>
> It will also factor general numbers, but is quite slow.
>
> It can be sped up for general numbers, but even then it aint that fast.

For general numbers, how does its work factor grow?
With the size of the factors?
With the size of the number being factored?

> Can anyone think of a serious use for such an algorithm, I mean one
> that might make use of its special powers? Of course I tried all the
> RSA prize numbers and a few other most wanted numbers floating around
> on the web, but obviously I should buy a lottery ticket if I thought I
> was going to be that lucky. I don't know if they have a caveat that
> says RSA primes shouldn't be chosen to be of that class, but they
> certainly should.

Are you sure it actually has special powers, before you try to
make use of them?

Phil

-- 
What is it: is man only a blunder of God, or God only a blunder of man?
-- Friedrich Nietzsche (1844-1900), The Twilight of the Gods