Ultimate EFF Prize Limit of GIMPS

[JuanTutors]

Originally Posted by R.D. Silverman

The issue is not intelligence, or lack thereof. It has NOTHING to do with
being smart.

The issue is doing one's homework. I assume that anyone sufficiently
interested in a subject will do background reading before indulging in idle
and ignorant speculation. And if one has NOT studied a subject, then,
to quote Tom Lehrer, "The least he can do is to shut up"

And, if you had bothered to read and understand my post, you would
realize that I already asnswered the question you now ask. Although a
formal proof is lacking, there is good reason to believe that no algorithm can
be faster than LL for *any* number.

Seeing the same ridiculous speculations over and over again about
"faster primality tests" from people who are clearly clueless about the subject
is TIRESOME.

Originally Posted by Prime95

Scrolling back, I see the post that really started this was a STATEMENT that AKS can be made "waayyyy faster".

I retract my defence of his wild claims. If it had been posed in the form of a question, then it should be answered politely - laymen should be able to get quick answers without understanding the complex theory behind the answer.

You really can't expect non-mathematicians study AKS. You guys really need to remember how high up and virtually inaccessible the understanding of this stuff is. Think about how seriously cursory a person's understanding of, say, the philosophy of Nietzsche is after reading the body of his work TWICE. You might not think it's cursory, but talk to a person who seriously studies his work and maybe you'll understand. And as cursory as your understanding is, when you discuss his work, don't you still make statements? Or do you always, always, always only ask questions?

[Prime95]

Originally Posted by dominicanpapi82

Plus, there's no reason to believe that some nice improvements on the AKS test can't make it waayyyy faster.

So you admit you have little to no understanding of AKS and make the claim above. Why?

It is admirable that you want to learn more about a topic you are unfamiliar with. Ask questions and learn. Wonderful. Your claim above could be read by dozens of people. Not knowing your background they may believe your claim and spread it - a nasty rumor begins.

[JuanTutors]

Originally Posted by Prime95

So you admit you have little to no understanding of AKS and make the claim above. Why?

It is admirable that you want to learn more about a topic you are unfamiliar with. Ask questions and learn. Wonderful. Your claim above could be read by dozens of people. Not knowing your background they may believe your claim and spread it - a nasty rumor begins.

I didn't really make a claim, did I? What I said was that there was no reason to believe that improvements on AKS can't make it "waayyyy faster". This is a forum, and people say things like that. If there if reason to believe that it can't be made way faster, then please tell us.

That's the problem here in mersenneforum. People forget that this is a forum. A person says something a little off, and instead of enlightening them and the rest of us we tend to criticize them and further use the chance to criticize all people who make any statements we don't like.

[Fusion_power]

Ewmayer,

I personally agree with your statement that the hardware we are using will improve over time. But just for the sake of discussion, I'll list the items that are likely to limit or prevent just such improvements. Please list what you think will be done to overcome them.

Just to get it out of the way from the beginning, I suspect that a radical new factoring algorithm or a primality test faster than LL is unlikely. That doesn't mean something won't be found.

1. You list continually increasing clock speed. But Intel is having very serious problems getting over 4 ghz. I think they will overcome that boundary, but don't think there is a new material on the horizon that can deliver more than 6 ghz. In effect, this limits processor speeds to about 50% faster than what we have today.

2. Multi-core processors are definitely on the way in. But a LL test requires serial processing, not parallel at least when considered at the level of testing an individual number. Even though it is possible to streamline the processing and gain improvement with multi-core technology, the overall throughput is unlikely to exceed a 100% improvement over todays implementation. A more likely result of multi-core processors is to have each core running a separate LL test so that say 8 tests could be running simultaneously on the same machine.

3. If the cache/bus/FPU is improved significantly, the FFT's would see a benefit. This would permit about a 500% improvement in testing speed for numbers over 100 million digits. As a possibility, we might get a 256 bit processor that writes direct to a 256 bit (or more) bus with say 32 meg of cache memory. There are a lot of ifs in producing such a processsor. More bits and more memory means more chance of something going wrong during production.


The way I see it, the best we could expect is about 30 times better than anything available today. With such a system, we could test a 1 billion digit number in a reasonable timeframe of less than a month. But the performance improvement becomes less and less effective as the numbers get larger. Somewhere around 100 billion digits, we would be looking at years per number tested. Granted this is dramatically better than anything we can do today, but how do you propose we go higher than this? Please note that I am not being entirely accurate with the math above, its just speculation so I played with the numbers pretty freely.

Fusion

[Prime95]

Originally Posted by dominicanpapi82

I didn't really make a claim, did I? What I said was that there was no reason to believe that improvements on AKS can't make it "waayyyy faster".

Yes, you did make a claim. The key words are "no reason to believe". Maybe there are very good reasons to believe AKS can't be made way faster. You don't know and I don't know.

I do agree with you that an erroneous post can be corrected in a polite manner. Save the big attack for a repeat offender.

[xilman]

Originally Posted by Prime95

Yes, you did make a claim. The key words are "no reason to believe". Maybe there are very good reasons to believe AKS can't be made way faster. You don't know and I don't know.

I do agree with you that an erroneous post can be corrected in a polite manner. Save the big attack for a repeat offender.

Given that this entire sub-thread is about a matter of phrasing, perhaps it may have been more correct to have said "I know of no reason why AKS can't be made way faster". That claim would, presumably, have been accurate and uncontroversial. It would have left open the possibility that others may know of a reason why it can or can not be so improved. It would also have given them the chance to enlighten us all --- I also see no reason why it can not be improved markedly in practice, nor any reason why it can. Even if the asymptotic behaviour we already know about, whether proven unconditionally or on extremely plausible conjectures, can not be bettered perhaps the proportionality constant can be improved substantially --- but I don't know whether this is the case or not. I have nothing to declare but my ignorance, to misquote Wilde.

Moral: it is often wise to examine the form of ones words used, as well as the concepts one is trying to communicate. It is far too easy to be misunderstood by people who read what they see rather than try to discern what may possibly have been meant.


Paul

[cheesehead]

... Plus, let's remind ourselves that natural language includes voice inflections, facial expressions, gestures, and other body language that is all lost from the plain text here. ... (censored)

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Originally posted by Prime95 I do agree with you that an erroneous post can be corrected in a polite manner. Save the big attack for a repeat offender.

I'll take that chance to attack Bob Silverman again, for his lack of understanding after repeated explanation.
It's clear that his meaning is not to actually ask a question.

xilman, Why dont you follow your own morals?
Sounds like you have the right idea, and now need to follow through with it.

[xilman]

Originally Posted by TTn

xilman, Why dont you follow your own morals?
Sounds like you have the right idea, and now need to follow through with it.

Please give an explicit example of where I have "not followed my own morals".


Paul

[R.D. Silverman]

Originally Posted by cheesehead

... Plus, let's remind ourselves that natural language includes voice inflections, facial expressions, gestures, and other body language that is all lost from the plain text here. ... (censored)

Yes! Indeed!

Which is exactly why posters must be careful in their use of language.
Mathematics is a language in which it is possible to say precisely what is
meant. In this forum, all we have is the verbatim text.

When posters fail to be precise in their language it can only be
for one of two reasons:

(1) They lack the competence and/or intelligence to express themselves
precisely.

(2) They are too lazy to bother.

Lack of competence is curable through training; *IF* they have the will to
undergo the necessary training. (and if they don't have the will, they should
leave, IMO)

There is little that can be done about lack of intelligence.

However, if they are too hurried or too lazy to be bothered formulating
their prose in a precise manner, then they deserve contempt and derision
(again, IMO)

[R.D. Silverman]

Originally Posted by xilman

It is far too easy to be misunderstood by people who read what they see rather than try to discern what may possibly have been meant.


Paul

I would argue that it is not the reader's job to try to discern what is meant.
It is the poster's job to make his/her precise meaning clearly understood by the audience.