"Rare" Primes

[Kevin]

Originally Posted by R.D. Silverman

The original query, as posed, used vague English words (e.g. rare prime) to
try to convey some mathematical idea. Mathematics is a domain of
knowledge in which it is possible to state PRECISELY what is intended.
The fact that the original poser used vague language and gave a very
poorly posed question is what makes clear that he lacks understanding of
mathematics.

Are you implying that anybody asking for "interesting" counterexamples, an "elegant" proof, or "instructive" examples doesn't understand math, because the quoted words don't have a precise mathematical definition?

[cheesehead]

Originally Posted by R.D. Silverman

I am not the one who labelled the response to the original question as coming from a moron.

... nor did I say you were. As I quoted, you wrote "I am afraid that YOUR original question shows that you are the moron." I.e., you labelled the original poster as a moron, and your posting is what I responded to.

And knowing the NAME of something is not the same as understanding it. (A paraphrased quote from Richard Feynman).

Lewis Carroll wrote something similar.

The fact that the O.P. knows the names of a few objects is not an indication that he understands mathematics.

No, but he not only knew the names, but also used them appropriately, and it was that _combination_, not merely knowing names, that I considered unlikely to come from someone lacking understanding: "The original question's appropriate uses of the mathematical terms ... are unlikely to have been composed by someone with a 'total lack of mathematical understanding'."

The original query, as posed, used vague English words (e.g. rare prime) to try to convey some mathematical idea.

So? This is a public online forum, not a professional journal or one of your classes.

Mathematics is a domain of knowledge in which it is possible to state PRECISELY what is intended.

So? This thread's posting content clearly involves ideas outside that domain as well as inside it.

And if you're requiring that all posts achieve some ideal of precision even outside of mathematics, then for consistency you need to disqualify a whole bunch (pardon the imprecision) of your own words.

The first response to the problem was a totally correct and precise response to WHAT WAS ASKED.

So? i don't dispute that.

And then the O.P. labelled the response as coming from a moron.

... and then you labelled the O.P. as a moron, which is not the first (or tenth, or twentieth, ...) time you've done that (i.e., labelling a poster as a moron) in forum threads.

I notice that you failed to chide the O.P. for his response.

You already did that, it seemed to me. I didn't see any use in piling on.

Can you say "double standard"??

When the O.P. has labelled other posters as "moron" without sufficient justification as often as you have in this forum, I'll treat him by the same, single, standard. I didn't complain the first several times you did it.

[Mini-Geek]

This warning should be put on every one of RD Silverman's posts...because any time he posts, it's just to insult someone who might not know as much as him or used improper language or something, to which somebody nicer tries to defend the insultee. The topic is always forgotten after RD Silverman posts, largely because he ignores it and starts a flame war based on something stupid.

[R.D. Silverman]

Originally Posted by Mini-Geek

This warning should be put on every one of RD Silverman's posts...because any time he posts, it's just to insult someone who might not know as much as him or used improper language or something, to which somebody nicer tries to defend the insultee. The topic is always forgotten after RD Silverman posts, largely because he ignores it and starts a flame war based on something stupid.

I am about to pour gas on the fire. I don't think that you are a moron.
I think that you are an idiot trying to become a moron.

I case you did not notice (and clearly you did not), I was DEFENDING
someone who the O.P. called a moron.

You clearly can not read.

[Visu]

Originally Posted by R.D. Silverman

The reply to your post was accurate. "rare prime" is a poorly conceived
notion at best because as the reply shows it is TRIVIAL to construct
subsets of the integers containing only finitely many
primes under according to some rule. I am afraid that YOUR original
question shows that you are the moron. It shows a total lack of
mathematical understanding.

It is also TRIVIAL NOT to construct subsets of the integers containing only finitely many primes according to some rule.How can you tell the difference in ALL cases.(I am assuming you haven't hidden away a proof that there are only finitely many Mersenne Primes somewhere for starters.)

[R.D. Silverman]

Originally Posted by Visu

It is also TRIVIAL NOT to construct subsets of the integers containing only finitely many primes according to some rule.How can you tell the difference in ALL cases.(I am assuming you haven't hidden away a proof that there are only finitely many Mersenne Primes somewhere for starters.)

Oh? We know that the are infinitely many primes in Z. We know that
there are infinitely many primes in (some) A.P.'s. Most (sufficiently)
fast-growing sequence will contain finitely many primes. It is known
that (with suitable definition of measure) almost all sequences
A_1, A_2, A_3, ... for which sum(1/log(A_i)) converges contain
finitely many primes (almost all means Lebesgue measure 1 among the
uncountable set of all such sequences; It is only the uncountability
of the sequences that makes this proof at all tricky.)

Constructing a sequence of integers that grows faster than linear that
contains infinitely many primes is NOT a trivial problem. We do have proofs for some. For example, there exists a positive real number theta such
that floor(theta^3^n) is prime i.o. I know of no equivalent proof that
the almost all sequences for which the above sum diverges contains
infinitely many primes. (I don't even know if it has been considered;
I just gave myself a research problem; but the proof MAY turn out to be
simple)

While it is virtually certain that the sequence (a^n -1)/(a-1) for n=2,3,5,...
contains infinitely primes for positive appropriate values of a (e.g. non-
powers) , we have no proof. Most FASTER GROWING sequences will not
contain infinitely many.

[R.D. Silverman]

Originally Posted by Mini-Geek

This warning should be put on every one of RD Silverman's posts...because any time he posts, it's just to insult someone who might not know as much as him or used improper language or something, to which somebody nicer tries to defend the insultee. The topic is always forgotten after RD Silverman posts, largely because he ignores it and starts a flame war based on something stupid.

It was not I who started the flamewar. It was the O.P.

If one wants to discuss mathematics, then either use proper language
or don't post. Failure to use proper language shows that either you
have not done proper backgound preparation or else lack the ability to
discuss the problem intelligently. In both cases you should not post!

I have been told repeatedly that this is not a classroom and that I am
not here to teach. If this is NOT a classroom, then it becomes a
(purported) discussion among peers. In that case flames are appropriate
for poorly posed questions or for posts that clearly show inadequate
ability/knowledge/preparation for intelligent discussion.

I propose we separate the math sub-forum into two groups:

(1) A discussion of mathematics at the undergrad or higher
level, with a requirement that anyone initiating a thread
has thoroughly mastered high school level math (basically
pre-calculus). I would also assume sufficient mathematical
maturity to present problems that make sense.
I would also presume that anyone posing a question
involving math not ordinarily seen in high school such
as abstract algebra, number theory, etc. has, AT A MINUMUM
at least read a book on the subject and worked some of the
problems.

This is basically a sub-forum for the mathematically
competent. It can even be refereed. It is the equivalent of
sci.math.research, except at a lower level.

(2) Questions, ideas, conjectures and general nonsense posed by newbies, and
those less knowledgeable. This would include those who can not rigorously formulate
their questions.

I fully promise not to even reply to this sub-group. It is the
equivalent of 'alt.algebra.help'

However, if newbies want to play with the big boys, they
need to show that they have earned the right to do so by
showing that they have at least read the literature before
posing any questions, and that they have formulated their
problem using standard mathematical notation and terminology.

There is a discussion currently in sci.math in which
others (not I) have made the statement: "You have not
earned the right to take up (or waste) my time" in reply
to a post.

John Baez created a score card for measuring cranks in general.
Some of his rules are quite relevant here. I will propose
some additional scores herein.

(1) 10 points for trying to discuss any subject for which
you have not taken a course, or read at least one book.

(2) 15 points for not using standard mathematical terminology.

(3) 15 points for failing to define your variables and their
domain.

(4) 20 points for trying to generate a discussion instead of
asking a question when it is clear that you do not understand
what you are trying to discuss.

(5) 25 points for failing to do a web or literature search
before posing an idea or question.

(6) 35 points for elementary mistakes in high school level
mathematics.

(7) 50 points for trying to invent new mathematical
terminology.

(8) 50 points for trying to "reinvent the wheel". An extra
10 points for reinventing a "square wheel" (e.g. a 'new'
algorithm that performs more poorly than existing ones)

(9) 50 points for posing poorly defined problems, or
for posing problems which show a lack of BASIC understanding
of elementary aspects of the subject you are trying to
discuss.

(10) 100 points for both trying to invent new terminology
and failing at the same time to rigorously define what
that terminology really means.

(11) 200 points for even trying to pose a solution to a
well-studied problem in which you are not an expert.

(12) 500 points for trying to claim that knowledge of the
state-of-the-art "gets in the way" of creativity.

(13) 1000 points for any comparison of yourself to any
well known mathematician, or for trying to point out that
some prior mathematican worked in some area in which he/she
was not trained as if this were an excuse for your doing the
same.

-- Note that there is a difference between asking "is the following
solution correct", and asserting that you have a solution.


I, in turn, will promise not to flame ANYONE unless their
crank score exceeds 25 (including both my scores and those
of John Baez).

If you want to discuss math at the undergrad level or higher,
you must earn the right to do so by demonstrating that you
have the background to do so intelligently. Otherwise, you
WILL get flamed. Above all, this means that any questions
presented need to be rigorous in their meaning.

[Visu]

Originally Posted by R.D. Silverman

Oh? We know that the are infinitely many primes in Z. We know that
there are infinitely many primes in (some) A.P.'s. Most (sufficiently)
fast-growing sequence will contain finitely many primes. It is known
that (with suitable definition of measure) almost all sequences
A_1, A_2, A_3, ... for which sum(1/log(A_i)) converges contain
finitely many primes (almost all means Lebesgue measure 1 among the
uncountable set of all such sequences; It is only the uncountability
of the sequences that makes this proof at all tricky.)

Constructing a sequence of integers that grows faster than linear that
contains infinitely many primes is NOT a trivial problem. We do have proofs for some. For example, there exists a positive real number theta such
that floor(theta^3^n) is prime i.o. I know of no equivalent proof that
the almost all sequences for which the above sum diverges contains
infinitely many primes. (I don't even know if it has been considered;
I just gave myself a research problem; but the proof MAY turn out to be
simple)

While it is virtually certain that the sequence (a^n -1)/(a-1) for n=2,3,5,...
contains infinitely primes for positive appropriate values of a (e.g. non-
powers) , we have no proof. Most FASTER GROWING sequences will not
contain infinitely many.

Strange that someone who demands precision uses terms such as "most(sufficiently)fast-growing" , "Most FASTER GROWING" and "virtually certain" to name a few.

[cheesehead]

Originally Posted by R.D. Silverman

I have been told repeatedly that this is not a classroom and that I am
not here to teach. If this is NOT a classroom, then it becomes a (purported) discussion among peers.

... or -- if this is not a classroom then it could, alternatively, be (and, in fact, is) a discussion among not-necessarily-peers of varying abilities and backgrounds -- a public forum with no entrance requirement or threshold.

In that case flames are appropriate

... but in other cases, they're not.

I propose we separate the math sub-forum into two groups:

A simpler alternative: create a subforum titled, "R. D. Silverman Answers Clearly-Phrased Questions Asked by Knowledgable Persons", or something similar specifying the requirement right in the title, to dissuade newbies from stumbling in by accident.

[Visu]

Originally Posted by cheesehead

... or -- if this is not a classroom then it could, alternatively, be (and, in fact, is) a discussion among not-necessarily-peers of varying abilities and backgrounds -- a public forum with no entrance requirement or threshold.

... but in other cases, they're not.

A simpler alternative: create a subforum titled, "R. D. Silverman Answers Clearly-Phrased Questions Asked by Knowledgable Persons", or something similar specifying the requirement right in the title, to dissuade newbies from stumbling in by accident.

I thought we already had a Miscellaneous Math Threads. Maybe all posts should go there by default and get voted into the main Math thread (by the moderators?) if enough people think the post has its merits.This will dissuade Dr Silverman from stumbling in by accident.

[Orgasmic Troll]

Originally Posted by Visu

Strange that someone who demands precision uses terms such as "most(sufficiently)fast-growing" , "Most FASTER GROWING" and "virtually certain" to name a few.

These are precise terms in mathematics. Go learn why.