From: Spike (spike66@attbi.com)
Date: Thu May 29 2003 - 23:09:05 MDT
>Spike just for idle ignoramuses like myself what is the basis
>(generally) for the interest in *really* big prime numbers and
>their discovery...
>I'm merely curious. Are there applications for this sort of thing?
>Why Spike, Why? Brett Paatsch
The topic came up on the Mersenne Search chat group: Guys,
why the hell are we doing this?
There were a number of responses, of which yours truly
won the grand prize for the most creative idea, this
prize being the heartfelt (if temporary) esteem of the
group.
My notion is that a long list of Mersenne primes could
be used as a gentle deterrence or a weapon of peace for
any extraterrestrial civilizations we might contact. If
we reveal our many resources, ET might be tempted to
come here and devour same.
But if we transmit a long list of Mersenne primes, (the
same in any base, in any corner of the universe) we
demonstrate that not only are we a clever species, we have
computer resources to simply waste on foolishness. This
could be easily extrapolated into our having a veritable
firehose of technology. One would be ill advised to give
humanity a reason to turn that firehose upon one.
(nice doggie, niiiice doggie, while backing away slowly.)
There are other reasons, such as THE MONEY! I could put
$100k to good use, couldn't you? Why not, it's a (nearly)
free lottery ticket. Furthermore, if you find one, you get
your name on a short list for all time, along with such
names as Euler, Pervushin, Woltman and Lucas.
Every time the group finds a new prime, you get to attend a
way cool math party with such luminaries as Donald Knuth and
Ernst Mayer. One must carefully rehearse not falling
prostrate upon the earth before them, crying plaintively
"Im so unworthy! I suck!" (They don't like it when you do
that in a crowded restaurant.)
I have reconnected with a lot of local math geeks either
directly or indirectly thru GIMPS.
Gregory Stock made a pitch at Extro4 about the effect
of cash prizes on research. We now have a perfect study
case. The EFF prize turned out to have little impact
that I can tell. The introduction of the Pentium 4
had a large impact however.
It is interesting to have a quantity that continues
to double in size every 11 seconds for years. The size
of the record largest prime doubles every 11 seconds
on average for long stretches of time (~1 million
decimal digit prime discovered on 27 Jan 1997, 2+ million
digit prime discovered 1 June 1999, 4+ million digit
prime discovered 14 November 2001. The doubling time
is actually getting shorter, as more people join GIMPS
and CPUs get dramatically faster. Since we are currently
searching near the 6 million digit mark, the doubling time
is now under 10 seconds. How many phenomena do you know
that exhibit hyperexponential growth, continuously
over long periods?
GIMPS reduces waste. If your background computing
cycles are not being used by something, your computer
is sitting there 99.9% of the time saying" whatdoIdo,
whatdoIdo, whatdoIdo... over and over. If you buy a
newer machine, it asks whatdoIdo much faster. We
should be WORKING those idle CPUs.
It pleases me to know my idle CPU cycles are being used
to advance science, even if in a kind of trivial way.
But not really *that* trivial. We are making a map of
nature here, a universal map. We don't know *for absolute
sure* that the abundance of primes continues to follow
logarithm rule for abundance. How would we know if they
mysteriously began to thin out once one is way out in
the kilothousand digit primes, beyond our ability to determine
primeness? Well, the Mersenne primes have that wonderful
shortcut to determine primeness, the Lucas Lehmer algorithm,
which allows a primality test to be done millions of
orders of magnitude more quickly than without it. In what
other area do you know of that you can even logically
use the phrase "millions of orders of magnitude" without
any exaggeration at all?
Mersenne Primes can be used to determine if your CPU is
running at the advertised speed, and with accuracy. The
GIMPS software logs whenever your computer drops a bit and
causes a checksum error. These checksums are performed
every couple hours or so. This way, if you get a checksum
that implies an error, the algorithm loses only a small
amount of processor time, going back to the last time
a reasonable checksum was found.
Heres the final thought. My friend Scott Kurowski
volunteered his company's services (irony: it is called
Entropia.com) to organize GIMPS. One would have to know
Scott. He is the kind of guy who has money magnetism.
If he walks thru a room, currency seems to chase him,
struggling to get into his pocket. A generous person is
he: at the last Mersenne party, he showed up and picked
up the bill. There were 14 of us present.
One wonders why Scott, the ultimate businessman, would
spend money in this way. Then it occurred to me that
GIMPS has generated a database of enormous value. Computers
dont make mistakes often, but they do make mistakes, and
the designs have bugs, such as the famous Pentium bug. GIMPS
has been quietly collecting data for several years now on
every kind of processor and every kind of operating system
that is in the world today. When your processor makes a
bad checksum, the result is logged. Scott can tell you
what processor is best, Intel, AMD or Motorola. He can
tell you if any particular operating system correlates
with more checksum errors. He can tell you which
combinations of processor and operating system works
best.
How much do you think this data is worth? To Intel? AMD?
Motorola? How about HP, Dell, Micron and Gateway?
Ive been meaning to ask Scott if he planned all along
to gather this database, or if it was just a fortunate
accident, an unintended byproduct. What do you think?
But for me, the biggest reward is being mentioned by the
highly esteemed Australian science writer Dr. Damien
Broderick, in his most intriguing and extropic book about
the future, The Spike, on page 87.
Of course, if I win the 100 kiloclams, that would surpass
the book thing as the biggest reward, but still the cite
is way cool.
{8-] spike
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