Author: Vincent Diepeveen
Date: 08:04:02 05/27/05
Go up one level in this thread
On May 27, 2005 at 10:37:50, Tord Romstad wrote:
>On May 27, 2005 at 08:28:12, Vincent Diepeveen wrote:
>
>>On May 26, 2005 at 16:37:48, Tord Romstad wrote:
>>
>>>It's not quite that bad. The current record prime was found on a single-CPU
>>>P4 2.4 GHz in 50 days. See the GIMPS ("Great Internet Mersenne Prime Search")
>>>page for details:
>>>
>>>http://www.mersenne.org/prime.htm
>>>
>>>Note that the world record primes are always Mersenne primes, i.e. prime
>>
>>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. the GIMPS project has what is it, a record
of 5 or 6 primes now at their conto?
This because they hardly have any competition.
>>GIMPS is like Gnuchess, they won't be staying forever on top.
>>
>>The advantage they had so far was that if you give all the 70000 computers or so
>>that are joining their prime search a job, that in a complete brute force
>>minimax way they can start proving the primes. Already in the 10 million digit
>>range they show how much of a problem they have with that.
>>
>>It's likely that GIMPS will be the first to find a 10 million digit prime. I'm
>>not so sure whether it will be GIMPS finding a 100 million digit prime though.
>
>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.
>However, I do have a strong interest in algebraic number theory (although
>it is not my field of research), and therefore know a fair bit about the
>mathematics behind the various techniques for factorization and primality
>testing (I am not an expert, though). That the theory can be used to
>create computer programs which can factor really big numbers and find
>enormous prime numbers is just a curiosity, nothing more. 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?
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.
>I don't care who finds the next big prime number, how much time the
>computation is likely to take, or even if a new world record prime is
>ever found. On the other hand, I *do* care if somebody is able to prove
>that there are infinitely many Mersenne primes, that no Mersenne number
>is divisible by a square, or that there are no odd perfect numbers. This
>is the kind of questions I am interested in.
>>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.
To factorize, he perhaps you're already done quickly, perhaps it's dividable by
23 who knows?
Hmm let's see 2^11 = 2047 ==> dividable by 23 :)
That's a far faster way to see whether something is a composite than doing the
lucas-lehmer test.
>>>For primes not of the form 2^p - 1, there is no test nearly as powerful
>>>as the Lucas-Lehmer test. As far as I know, the most efficient known
>>>algorithm is ECPP (elliptic curve primality proving). Using this test,
>>
>>Let's not confuse a special type prime with general primes. Most 'tests' work
>>for all primes. Lucas-Lehmer works ONLY for mersenne.
>
>That's exactly what I said in the paragraph you quote.
>
>>With some highschool math i found another way to quickly determine Mersenne
>>numbers with a big exponent:
>> // test whether m = 2^p - 1 is prime, note p is also prime.
>> t = 3;
>> for( j = 1; j < p ; j++ )
>> t = t*t; (mod p)
>> if( t == p-3 ) printf("prime\n"); else printf("composite\n");
>
>You must have a bug or a typo somewhere, I think. The code above will
>definitely not work. It fails even for p=5, as you can verify just by
>calculating in your head.
Bugfix your head :)
3
9
19
20
28 <==> p-3 = 31 - 3 = 28
>>The fastest probabilistic test possible for a special prime will most likely be
>>not faster than Lucas-Lehmer.
>
>This is probably correct, but of course the probabilistic tests have
>the obvious advantage that they work for all numbers, not just Mersenne
>numbers.
>
>Tord
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