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Subject: Re: Money winning primes ($100k+)

Author: Tord Romstad

Date: 02:40:12 05/28/05

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On May 27, 2005 at 11:04:02, Vincent Diepeveen wrote:

>On May 27, 2005 at 10:37:50, Tord Romstad wrote:
>
>>On May 27, 2005 at 08:28:12, Vincent Diepeveen wrote:
>>>
>>>How much money are you willing to bet on this indoctrination attempt by the
>>>GIMPS guys?
>
>>What indoctrination attempt are you talking about?  I provided a link to
>>the GIMPS site in order to inform about the hardware and software used to
>>find the currently biggest known prime number, and also because it contains
>>a number of useful links for those who are interested in learning more
>>about Mersenne primes and prime numbers in general.
>
>"world record primes are always Mersenne primes"
>
>that's a very rude statement and just wasn't true in the past and most likely
>won't be true in the future either.

Point taken -- I should be careful to use strong words like "always" without
adding qualifications.  In the quoted sentence above, it would definitely have
been better to write "almost always" or to add the word "recently" somewhere.
If I recall correctly (and it is very possible that I don't) a non-Mersenne
number
has been the biggest known prime only once in the computer era.  It could
happen again, of course, though I think Mersenne primes will still top the list
most of the time.  At any rate, I apologize for the inaccuracy.

However, I still don't see what this has to do with GIMPS.  They can just
drop the letter 'M' from their name and search for non-Mersenne primes
as well if they prefer.

>the GIMPS project has what is it, a record of 5 or 6 primes now at their conto?

I have no idea.

>This because they hardly have any competition.

Yeah.  Prime hunting will never be among the world's biggest and most
popular sports, I guess.  :-)

>>I couldn't care less who or what finds the first 10 or 100 million digit
>>prime number.  World record prime numbers in themselves hold absolutely
>>zero interest for me.
>
>I am not careless about such huge achievements.

Like most people, I tend not to care much about huge achievements in
fields in which I don't have much interest.  For instance, becoming an
Olympic champion in badminton is arguably a much bigger achievement
than finding a world record prime number (because the competition is
much harder), but I still don't care who wins in the next Olympic games.

>>Actually spending thousands of CPU hours hunting for new world
>>record prime numbers seems like a tremendous waste of time to me.
>
>Please tell me, what do you consider useful ways to spend system time?

Easy:  Whatever ways you or your employer considers useful.  This is
an entirely subjective question.  I often spends lots of CPU time running
matches between computer chess programs, which almost everybody
on the planet except those reading this forum would consider a waste
of time.

If you meant to ask me about examples of tasks similar to prime
hunting which I would consider more interesting (and again, this is
nothing more than a subjective opinion), I would suggest searching
for an odd perfect number as a good example.  After all, we know
that there are infinitely many prime numbers, but we are still not
sure whether there exists odd perfect numbers.  From a mathematical
perspective, finding a concrete prime number bigger than all those
previously known is rather dull and unimportant, while finding an
odd perfect number would be a surprising and very important
number-theoretic discovery.

>Note that research after new medicines and other bio-medical researches eats
>less than 0.5% system time.
>
>I remember a research, trying to predict the future height of the ocean, running
>on a big 1024 processor supercomputer here in Netherlands. After putting in half
>a million hours of cpu time (yes that was many months of non stop computing at
>hundreds of processors), they concluded that the sea would rise 1 meter.
>
>1 month later i found in a logfile of them: "small initialisation bug, we
>initialised the ocean water height 1 meter too high".
>
>But was it wasted system time?
>
>The researchers got their publicity world wide and their own discovery show that
>the ocean floor 'soon' will rise 1 meter.

Cool story!  :-)

>>>Factorization goes faster than proving,
>>
>>I am sure you meant to say the opposite, as is evident from the rest of
>>your post.  Testing whether a big number is prime is much less work than
>>actually factoring the number (which is also intuitively obvious).
>
>Please reread what i wrote. It's far easier to get rid of a big % of composites
>by first factorising. To prove 1 number you'll have to do a million or 33+
>million FFT calculations.

Sorry, it wasn't clear to me what you meant.  It now seems that that you only
meant looking for one small factor of a huge number, not about finding a
complete factorization.  In this case I agree with you, of course.

Tord



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