Fun with big numbers

[Aaron Blosser]

At last, something I saw while looking through the online archives that
I know something about. :)

Mersenne Numbers, 2^p-1, are interesting because it's relatively easy to
determine primality (indeed, only 38 known) of them by using some fun
advanced number theory, the Lucas-Lehmer test.

It's a simple algorithm really, and well suited to computers.

Still, the current numbers being tested (I currently have mine testing
2^13047077-1) can take about a month even on a 1GHz Pentium III.
Pentium 4's (1.7GHz for example) due to some really neat optimizations,
can do the same number in about 12 days.

Why do people do it?  Well, number theory is interesting to some folks,
just like philatelists or numismatists have their own hobbies.

The fact that the EFF has a prize for finding the first megadigit prime
(which was found last year), and the first 10-megadigit, 100-megadigit,
etc. is also compelling to some.  Odds of finding one are small, and
since the 10-megadigit candidates can take over a year even on the
fastest computers, I doubt we'll find one anytime soon.

There's also a strange fascination with trying to determine if there's a
pattern.

Mersenne found a few new ones in his time, but of course as ways to
calculate much larger numbers were discovered, Mersenne was shown to be
wrong about some that he claimed were primes.

The last 4 Mersenne Prime's discovered were found by GIMPS (Great
Internet Mersenne Prime Search) (www.mersenne.org/prime.htm).  They also
have links to the EFF prize stuff.  If you are bored with current
distributed computing projects, or if your computers lack the bandwidth
to handle SETI data (or just don't believe in alien life), GIMPS might
be an interesting alternative, at least for x86 based platforms.
Non-automated (and non-optimized) clients exist for other platforms, but
the Win32 version can send/receive results and is highly tuned to the
x86 platform in it's various incarnations.