Ultimate EFF Prize Limit of GIMPS

[xilman]

Originally Posted by R.D. Silverman

And if one has NOT studied a subject, then,
to quote Tom Lehrer, "The least he can do is to shut up".

The original statement by Tom Lehrer is:

"I feel that if a person has problems communicating the very least he can do is
to shut up."

Do you ever get the feeling that you're just not getting through to some people --- the ones who keep on posting uninformed speculation on mathematical topics?




Paul

Once more, please check that your irony detector is working correctly before responding.

[ewmayer]

Originally Posted by cheesehead

I once heard an interview in which Warren Buffett was quoted as replying, after having been asked what constituted wisdom, something like (this is my paraphrase) "Wisdom consists of having as many different models as possible, so that one may choose the most appropriate model to apply to any given situation."

"Wisdom consists of having a vast mental reserve of as many pithy-sounding yet basically meaningless aphorisms as possible, so that one may choose the most appropriate throwaway phrase with which to impress the clueless in any given situation."

[Prime95]

Originally Posted by R.D. Silverman

The issue is doing one's homework.

Posting a question here could be viewed as a very quick way of doing your homework. Yes it may be lazy, but the poster may view it as the most time-efficient way to get the answer to his question.

[R.D. Silverman]

Originally Posted by Prime95

Posting a question here could be viewed as a very quick way of doing your homework. Yes it may be lazy, but the poster may view it as the most time-efficient way to get the answer to his question.

Except that the poster would not be able to UNDERSTAND any answer
without having first done the necessary background reading.

[R.D. Silverman]

Originally Posted by xilman

Do you ever get the feeling that you're just not getting through to some people --- the ones who keep on posting uninformed speculation on mathematical topics?

Certainly! I am well aware that I am not getting through. But to use
another aphorism: If at first you don't succeed, try, try again.

The following should be required reading of everyone who posts here:

J. Kruger & D. Dunning
Unskilled and Unaware of It: How Difficulties in Recognizing One's Own
Incompetence Lead to Inflated Self-Assessments.

J. Personality & Social Psychology 1999

Most of the posters here are truly unaware of how much it is that they DON'T
know in the subject area of this forum. They ask questions and are unaware
that they lack sufficient competence to understand the answers to what they
ask. This is one reason why I try to encourage people to READ TEXTBOOKS
ON THIS SUBJECT.

I recognize all too well that this is a forlorn hope. Too many of the posters
are simply academically lazy and have neither the will, the attention span,
or the dedication to do the required reading. Learning this material is HARD.
But if one is truly interested then the reward is worth the effort. And
speaking only for myself, I don't want to be bothered by those who are
unwilling to make the effort.

We have all heard the old joke:

A first-time visitor to New York City stops a policeman on the street and
asks: How do I get to Carnegie Hall?
Ans: Practice, Practice, Practice.

Learning what is necessary to discuss this subject also requires Practice,
Practice, Practice. And too many are unwilling to commit the time. They
want the reward and recognition of participating, without putting in the
needed work. And I think this attitude sucks.

[Prime95]

Originally Posted by R.D. Silverman

Except that the poster would not be able to UNDERSTAND any answer without having first done the necessary background reading.

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.

[Numbers]

Originally Posted by R. D. Silverman

And I think this attitude sucks.

And I think this attitude sucks too.

But I also recognise it as a symptom of the instant gratification generation who believe that because they can google almost anything then all that "knowledge" is out there at their fingertips. It's the downside to the "advances" in technology that have turned childs play from an exercise in imagination where three sticks and a blanket can be a space-rocket one day and an Indian teepee the next into an activity requiring no more intellectual input than inserting the batteries.

Whatever your response, I for one am delighted that you are at least participating in the discussion.

[cheesehead]

Ernst,
"Wisdom consists of having a vast mental reserve of as many pithy-sounding yet
basically meaningless aphorisms as possible, so that one may choose the most appropriate
throwaway phrase with which to impress the clueless in any given situation."

In chess problem composition, that would be termed a [I]dual[/I], I think. :smile:

(spoilerized because of increasing off-topicness)

[Fusion_power]

In my particular area of expertise, I am considered an expert, one of maybe a dozen people in the world with a particular set of skills. Yet I can see my knowledge and understanding increase as each year goes by. The more I know, the more I know that I can't possibly know all that I wish.

I would ask Bob what he has done to improve his understanding lately? What are you doing as your "homework" Bob?

Please don't misinterpret this question. Its asked in all sincerity.

Fusion (Darrel Jones just so you won't think I'm hiding who I am)


P.S. to get back on topic, I have seen nothing yet to indicate that we will be able to test numbers > @100 million digits in a reasonable amount of time unless a significant breakthrough is made on some new algorithm or some radical computer design changes the landscape.

[ewmayer]

Originally Posted by Fusion_power

P.S. to get back on topic, I have seen nothing yet to indicate that we will be able to test numbers > @100 million digits in a reasonable amount of time unless a significant breakthrough is made on some new algorithm or some radical computer design changes the landscape.

Why? When something akin to the Cell processor (i.e. a CPU with on the order of 10 computational cores, each with decent 64-bit floating-point and/or integer functionality) becomes widespread in the PC world, even with no increase in clock rates that would increase the per-CPU throughput by an order of magnitude. Add the fact that clock speeds will continue to increase and you've got a second factor of 10-ish speedup, allowing you to test a 100Mdigit number in under a month, without requiring any huge algorithmic breakthroughs, just good CPU-adapted software implementation of current algorithms. Where's the fundamental problem you allude to?

[jinydu]

Originally Posted by R.D. Silverman

A Theorem of Pomerance shows, essentially that we can never hope to
do better than O(lg N) multiplications in any test. All we might do is reduce
the implied constant. His theorem places a bound on the size of a primality
proof certificate.

So there is a rigorously proven bound on how fast any deterministic primality test for any natural number of any form can ever get?