Poll: Ultimate Limits of GIMPS

[jinydu]

In reference to a post that was mentioned in a previous thread, I'm asking this question: What is the highest speed that GIMPS will ever attain?

Comments are appreciated.

[alpertron]

The speed of the project will be increasing as the computers are being more powerful.

Maybe a better poll is about the number of users who run GIMPS. Will it increase or is it near the peak?

[jinydu]

I see a lot of optimistic votes. Maybe I should have included another option, such as 100 - 200 teraflops.

Would Mr. Woltman like to give an estimate?

[Peter Nelson]

Are we only considering how far the GIMPS project can go while limited to existing x86 processors?

That is all that is available currently.

Performance per watt will increase but not THAT much. So it might be expensive on your electricity bill to sustain such very high levels of throughput using x86 and this will act as a disincentive or ceiling on work.

Or can we include powerpc and future alternatives eg special purpose math processors?

If it is any architecture I think we can go well beyond 100TFLOPS one day.

[pacionet]

My question is : can GIMPS sustain the rate of exponents growth ?
Nowadays an exponent takes some months to be verified , in future it will probably take longer and longer because in my opinion exponents size grows faster than PC performances.
When the fastest PC will take 2 years to check an exponent , does GIMPS make sense ?

[R.D. Silverman]

Originally Posted by pacionet

My question is : can GIMPS sustain the rate of exponents growth ?
Nowadays an exponent takes some months to be verified , in future it will probably take longer and longer because in my opinion exponents size grows faster than PC performances.
When the fastest PC will take 2 years to check an exponent , does GIMPS make sense ?

What is it that compels people who clearly have no understanding of a
subject to spout vague and meaningless generalities?

(1)
"In the future it will probably take longer and longer"

The subject here is mathematics. "longer and longer" is vague and
meaningless.

(2) Your "opinion" isn't worth much. We do not do mathematics by
popular poll or by "opinion". Look at the time complexity required to
check a single exponent. Make an estimate of increases in machine
speed. Make an estimate of increases in the *number* of participants.
Apply a little arithmetic. This will tell you whether your "opinion"
is correct.

(3) Do you even know how long it takes to check a single exponent p
as a function of its size? NO? Then you are not entitled to even HAVE
an opinion on this subject.

Hint: multiply the number of required multiplications and the time to
do each multiplication. What do you get?


I also suggest that you check the history of this project. Once, exponents
were smaller and machines a lot slower. How long do you think a PC took
to check an exponent (say) 5 years ago? If you don't know, then how can
you have ANY opinion on whether time to check an exponent on a single PC
will either increase or decrease in the future??? Do you know how
long a (say) 3GHz Pentium takes now to test an exponent at the size
of the (say) 5000 smallest untested exponents today?

Hint: It takes ~125 hours. It will be a long time before we reach the point
where it takes "2 years".

What is it that compels people to spout nonsense before checking FACTS?

I do acknowledge: I do not understand people.

[jinydu]

Originally Posted by pacionet

My question is : can GIMPS sustain the rate of exponents growth ?
Nowadays an exponent takes some months to be verified , in future it will probably take longer and longer because in my opinion exponents size grows faster than PC performances.
When the fastest PC will take 2 years to check an exponent , does GIMPS make sense ?

Has the speed been growing exponentially at all over the past year and a half?

http://mersenne.org/ips/stats.html

hasn't been updated since May 2004.

Also, since the majority of people think that GIMPS will one day break 100 Teraflops, what do you think is the highest speed it will ever reach?

[Mystwalker]

Originally Posted by R.D. Silverman

The subject here is mathematics.

Actually, this is the Lounge - thus I would say he's talking conversationally, not mathematically.

I do acknowledge: I do not understand people.

Maybe it helps when you take the possibility into account that a certain amount of members here are still quite young (< 16 years?) and/or don't have any experiences in algorithmic complexity. In addition, I think that many people "enjoy" using as few math as possible in their free time (I can almost feel your pain here, it disturbs me, too).

But I kind of understand your bewilderness - I almost feel physical pain when reading dreadful spelling mistakes, e.g. "standart" (very common nowadays) or the classic: the superlative of unique ... should be something like "the uniquest" in english.

[R.D. Silverman]

Originally Posted by Mystwalker

Actually, this is the Lounge - thus I would say he's talking conversationally, not mathematically.



Maybe it helps when you take the possibility into account that a certain amount of members here are still quite young (< 16 years?) and/or don't have any experiences in algorithmic complexity. In addition, I think that many people "enjoy" using as few math as possible in their free time (I can almost feel your pain here, it disturbs me, too).

But I kind of understand your bewilderness - I almost feel physical pain when reading dreadful spelling mistakes, e.g. "standart" (very common nowadays) or the classic: the superlative of unique ... should be something like "the uniquest" in english.

I have no problem with: "I think that many people "enjoy" using as few math as possible in their free time"

But if they enjoy using as little math as possible, why post to a forum
devoted to a discussion of mathematical subjects???

It's not just lack of mathematical knowledge. That problem can be corrected.
The problem is that people who are clearly ignorant of a subject seem to
insist to posting their own "opinions".

I'd like to understand what compels such people!

If I find myself interested in a subject, I take the time to do at least
some studying before making pronouncements or offering an "opinion".

I also find surprising that some people think that "opinion" matters
in mathematics. Math is not done by "opinion". If someone has an
argument to present, then show us your mathematics! But don't post
hand waving "opinions".

[Mystwalker]

Originally Posted by R.D. Silverman

The problem is that people who are clearly ignorant of a subject seem to insist to posting their own "opinions".

Hm, maybe it's just plain lazyness?

[xilman]

Originally Posted by R.D. Silverman

I also find surprising that some people think that "opinion" matters in mathematics. Math is not done by "opinion". If someone has an
argument to present, then show us your mathematics! But don't post
hand waving "opinions".

I find it surprising that you find that surprising, and that mathematics is not done by "opinion".

In my opinion, the Riemann hypothesis is true. It appears to be the opinion of many other mathematicians, so much so that many many results are published which are conditional on the RH and its various extensions.

Ok, I'm deliberately taking a contrary position for the point of argument, but I'm not doing it frivolously or merely to annoy. My intent is to illustrate that a conjecture in the mathematical sense is but an opinion. It may be (and certainly should be) backed up by a great deal of evidence and reasoning but until it or its negation is converted into a theorem a conjecture remains an opinion.


Paul