"Rare" Primes

[Visu]

Originally Posted by R.D. Silverman

Hey moron! Go learn some mathematics. I *defined* what sufficiently
fast growing meant: i.e. sum (1/log(A_i)) *converges*. 'most' is certainly
well defined as is 'virtually certain': go learn some measure theory.

I did not question your lack of definitions. I questioned your use of "most" and "virtually certain" as qualifiers. Why didn't you say "all" instead of "most" and "certainly" instead of "virtually certain"?

The OPs original query may have been poorly phrased but it does have its merits. For example while there are only 3 known Wilson Primes it has been conjectured that infinitely many exist. He only seemed to be asking if he has missed any from his list.

Originally Posted by R.D. Silverman

Learn what it means to be a set with asymptotic density 0. Learn
the precise meaning of 'occurs with probability 1'.

A finite set HAS to have an asymptotic density 0, but having an asymptotic density 0 does not mean that the set is finite.

I am not certain where the 'occurs with probability 1' comes in.

[R.D. Silverman]

Originally Posted by Visu

I did not question your lack of definitions. I questioned your use of "most" and "virtually certain" as qualifiers. Why didn't you say "all" instead of "most" and "certainly" instead of "virtually certain"?

The OPs original query may have been poorly phrased but it does have its merits. For example while there are only 3 known Wilson Primes it has been conjectured that infinitely many exist. He only seemed to be asking if he has missed any from his list.



A finite set HAS to have an asymptotic density 0, but having an asymptotic density 0 does not mean that the set is finite.

I am not certain where the 'occurs with probability 1' comes in.

Sigh. You need to read my signature. It pertains to you. I did not say "all", because it would be incorrect. A subset (of an infinite set) with density 1
need not contain ALL elements. I did not say "certain" because it too would be incorrect. A probability sub-space can have measure 1, yet not
contain ALL elements of its parent.

And where in hell did I ever say that a set has to be finite to have density 0???

And your ignorance clearly shows in your lack of understanding of the
relevance of "probability 1".

Once again, GO STUDY SOME MEASURE THEORY.

[Housemouse]

I am sorry that I overreacted to the first reply to my post, I mistakenly thought he was being sarcastic.

I did not intend to start a flame war.

I am sorry I lack the mathemtical knowledge RDS demands of everyone.

Although I lack mathematical knowledge, I am very curious about prime numbers.

I will try to improve my future posts.

RDS, please do not waste your time reading my future posts; they will probably not meet your criteria. If you do not read them; we both will be happier.

Thank you

[davieddy]

Well said Housemouse.

[cheesehead]

Originally Posted by R.D. Silverman

It is fair for competent people to ask that such a forum be labelled as such so that we don't waste our time.

You have had years in which to learn that this forum has postings by those you deem incompetent and ignorant, yet you still lack the self-control to avoid wasting your time by responding to questions by those you deem incompetent.

If you were in full control of yourself, you could refrain from responding to questions you deem inadequate to meet the standards you espouse. I've pointed out to you that there are other participants who are willing to take the time and effort to respond to those questions in a different manner, so you need not fear that anyone's questions will go unanswered. That you continue to pester folks here in the way you do is a sign that you either have an uncontrolled emotional compulsion to respond, and/or that you use this forum to express anger that would otherwise leak out in other areas of your life.

There is no way to know, a priori, whether a post contains meaningful content until after one has read it and digested its intent. By then, of course, one has already wasted the effort.....

But at that time you could still choose not to waste further time and effort, by the simple choice of not composing and posting a response. You're certainly capable of figuring this out, yet you continue to waste that further time and effort by posting your responses to those. Clearly, then, you are not making a rational decision, but are driven by irrational forces beyond your conscious control.

If you want the math sub-forum to remain 'one size fits all', then you can continue to expect flames.

... from people who cannot control themselves according to their own publicly-expressed criteria!

[Orgasmic Troll]

Originally Posted by xilman

Not obviously a bad idea.

Are there enough moderators willing to put in the effort?

I'd help out and Bob certainly should! He's often shown himself willing to help the intelligent but uneducated. If he doesn't flame anything in the MMT and moves out of there anything he considers worthwhile, that sounds like a valuable service to me.

On the other hand, flame wars do provide entertainment for by-standers who are mature enough not to be fazed by them and trolling is a well-established pass-time, one in which I indulge myself every now and again including here.


Paul

I don't do much moderating in Misc. Math (I haven't seen things get out of hand, and threads that I think should get moved out usually get snapped up by another mod before I get to them) and I'd be willing to filter through messages and kick them over here if they seem worthy

[robert44444uk]

Oh dear, this has become a sad thread.

I usually score quite highly (crankometer) on many of my questions I pose to this group. I persevere because I quite like recreational maths, and I am always grateful for helpful responses. I like to be enlightened. And some responders are better than others in bringing out the best in me.

But I persevere also here because I have a relatively thick skin. I duck and weave the unpleasant.

My preference is to receive thoughtful responses that both educate and encourage.

I think the forum already has two types of sub groups, and threads usually belong to either one or the other, so there is no real need to change.

This is a lively group and there are some great and helpful minds out there. It would be good to keep it that way.

[gd_barnes]

Well, it's nice to know I'm not the only one who starts flame wars.

I have an idea. Why doesn't everyone start responding to the question that was originally posed. Even if it's not worded quite the way it is needed for precise mathematics, to me it's clear what the O.P. intended:

Find prime forms with few primes but be reasonable about it by not allowing such outlandish forms that they become large very quickly. In other words, don't make it some stupid form that gets large so quickly that while it cannot be proven to never have a prime, it has such a miniscule chance that it is uninteresting for mathematical discussion.

RDS, I realize this is still very vague. I'm only stating what it APPEARS that the O.P. intended. I claim no understanding of math higher than high school calculus and freshman level algebra.

This appears to be an interesting topic to expound upon. Let's set up some parameters and rules about what constitue an 'interesting rare prime form', i.e. not something stupid like k*2^(n^n^n^n^n^n)-1. Then go from there. The O.P. gave us a starting point with some interesting forms. We just need to frame the parameters for 'rare primes' of other forms.


Gary

[R.D. Silverman]

Originally Posted by gd_barnes

Well, it's nice to know I'm not the only one who starts flame wars.

I have an idea. Why doesn't everyone start responding to the question that was originally posed. Even if it's not worded quite the way it is needed for precise mathematics, to me it's clear what the O.P. intended:

Find prime forms with few primes but be reasonable about it by not allowing such outlandish forms that they become large very quickly. In other words, don't make it some stupid form that gets large so quickly that while it cannot be proven to never have a prime, it has such a miniscule chance that it is uninteresting for mathematical discussion.Gary

Sigh. You need to read my signature. It applies to you.
No matter how many times I say it, the message does not appear
to get through to some people.

It does not take knowledge of ANY advanced mathematics to see
that you are spouting VAGUE GIBBERRISH. It isn't math, it is
NONSENSE. Without a definition of the terminology involved, what
you say is MEANINGLESS.

What does "be reasonable about it" mean?
What does "outlandish" mean?
What does "stupid form" mean?
What does "uninteresting" mean in this context. And who is the
audience? Wannabees? Cranks? Or real mathematicians???

The O.P. did not ask a question that CAN be answered in
any meaningful way.

[Housemouse]

I am not a mathematician. I only had 3 years of high school math. But I am curious. I defined what I meant by "rare" for the purpose of this thread.

Is it so easy, as to be trival, to construct formulas that you can prove will result in exactly 1 prime, 2 primes etc. up to 10?

[Wacky]

Originally Posted by Housemouse

Is it so easy, as to be trival, to construct formulas that you can prove will result in exactly 1 prime, 2 primes etc. up to 10?

Yes! It is trivial to create a function that will generate any finite number of values. By selecting a set of prime values to be generated, the resulting formula will meet your criterion.