Del Brand <[EMAIL PROTECTED]> wrote:
>I always get asked what is the purpose or use for such large prime
>numbers. Since I'm not a math geek, I don't know what to tell them.
Well, the prime numbers GIMPS has discovered are so overwhelmingly
large as to make them completely impractical for (present-day)
cryptographic purposes that the old saw about "more secure cryptography"
doesn't hold water. I always tell people that it's not the numbers
themselves that are of practical importance - rather, it's the algorithms
that are developed to manipulate them efficiently that are important.
For example, efficient large-integer arithmetic is important both in
basic number-theoretic research and in applications such as cryptography.
Fast transform arithmetic (which we use to perform the large-integer
multiplies that are the rate-limiting operation in most primality-testing
algorithms) has a huge range of applicability, from the signal processing
that goes on every time one makes a call on a mobile phone to analysis
of scientific data. Being able to squeeze a factor of 2-5x in speed
out of one's CPU (the typical speed ratio of the GIMPS' clients' FFTs
versus various "industry standard" FFTs like that in Numerical Recipes
or the like) via a well-crafted hardware implementation of the algorithm
is also a useful thing.
Personally, I need no immediate practical justification - I just find
working at the interface between number theory and computer science to
be endlessly fascinating - but for those who do, there is no lack of such.
Cheers,
-Ernst
