I already know I'm a kook, but humor me.

[Orgasmic Troll]

Originally Posted by Wacky

With what?
•The rest of us all understand your reaction.
•We've all seen Mr. Silverman's style many times.
•Mr. Silverman will probably not change his style any time soon.
•Try to ignore whatever Mr. Silverman writes except …
•Dr. Silverman is a well-respected professional mathematician
•His mathematical statements are very reliable and trustworthy.
•Just skip over all he writes about … that is not purely mathematical.

I cannot decide whether I agree or disagree with you. Your statement lacks the clarity that Mathematicians require in order to understand it.

I'm not picking on you. Your comment, at a minimum, indicates that you understand that individuals may disagree, but can remain civil in that disagreement.

But, particularly in Mathematics, clarity is very important.

I thought it cheesehead's sentiment was "obvious to the reader" and did not think it necessary to expound on my disagreement.

Cheesehead presented three main statements and several supporting points. I disagree with the three main statements:

1) The rest of us all understand your reaction.

While I understand it, I don't agree with the implied message that I (being included in "we") condone his reaction.

2) I recommend that you just try to ignore whatever Mr. Silverman writes except for the portion that consists of purely mathematical statements.

I believe this statement is the crux of cheesehead's message and I disagree with this recommendation. I think it would be more worthwhile to try and see things from Dr. Silverman's perspective and understand why your actions would inspire such brusk responses. While I may disagree with Dr. Silverman's delivery, I rarely disagree with the message.

[cheesehead]

TravisT,

I specifically addressed that posting to jasong because I tailored the content for jasong.

My intent was (as it has been in the past) to reduce unnecessary newbie-expert conflict in this forum. Working toward that goal involves making statements addressed to various participants; this time it was to jasong.

When I wrote "The rest of us all understand your reaction" I was deliberately being more inclusive than precise because I judged that better suited for the purpose of my message.

Interpreting my use of "understand" to imply "condone" was your choice, and you happen to be mistaken about that particular choice in this particular case.

I agree that it can be worthwhile to contemplate Dr. Silverman's perspective, but I did and do not think it would have been helpful (for the purpose of this particular message) to include that idea this time.

Thank you for your calm responses.

[trilliwig]

Originally Posted by mfgoode

The formula you have given is a powerful one. I have not come across it in the 'Music of the Primes'
Could you please refer me to an appropriate web site or book which derives this formula? Thanks

Try googling for Lucas sequences.

--
Sam

[mfgoode]

Originally Posted by trilliwig

Try googling for Lucas sequences.

--
Sam

I tried but did not get the formula in question
Mally

[Numbers]

Originally Posted by mfgoode

There are minor errors in your post.

Mally, welcome back from your holiday. I heard about the flooding in Mumbai and was thinking of you. Hope all is well.
Thank you for pointing out the small mistake with regard to his name, obviously I meant Lehmer.

Originally Posted by mfgoode

Also the LL test deals with Mersenne primes only and not with any odd prime.

I believe that this is not quite correct. It was developed specifically for that, but if you look here:
http://mathworld.wolfram.com/Lucas-LehmerTest.html

you will see that it can also be used for other primes – though admittedly in a slightly different form. What I actually meant to say was that where n = 2^p-1, Lucas showed that p (not n) = 1(mod 4), but Lehmer extended the proof to all p.

You will find the discussion of this on p. 206 of “The Music of the Primes”, but he doesn’t do much more than discuss how the L/L numbers are calculated. For the particular form of the equation I used in my post I am indebted to Dougy, who posted it here:
http://www.mersenneforum.org/showthread.php?t=4508

in a previous discussion on this topic, where you will also find some references.

[Orgasmic Troll]

Originally Posted by cheesehead

TravisT,

I specifically addressed that posting to jasong because I tailored the content for jasong.

My intent was (as it has been in the past) to reduce unnecessary newbie-expert conflict in this forum. Working toward that goal involves making statements addressed to various participants; this time it was to jasong.

When I wrote "The rest of us all understand your reaction" I was deliberately being more inclusive than precise because I judged that better suited for the purpose of my message.

Interpreting my use of "understand" to imply "condone" was your choice, and you happen to be mistaken about that particular choice in this particular case.

I agree that it can be worthwhile to contemplate Dr. Silverman's perspective, but I did and do not think it would have been helpful (for the purpose of this particular message) to include that idea this time.

Thank you for your calm responses.

Coming from my perspective, I see a lot of myself in the newbies and I'm starting to see more of myself in Dr. Silverman's responses. I think there's quite a wide gap in understanding from both sides, the newbies can't understand why Dr. Silverman's responses are so harsh, and Dr. Silverman is too far removed from his newbie days to see himself in the newbies that post here.

Just a theory, lots of assumptions.

[R.D. Silverman]

Originally Posted by TravisT

Coming from my perspective, I see a lot of myself in the newbies and I'm starting to see more of myself in Dr. Silverman's responses. I think there's quite a wide gap in understanding from both sides, the newbies can't understand why Dr. Silverman's responses are so harsh, and Dr. Silverman is too far removed from his newbie days to see himself in the newbies that post here.

Just a theory, lots of assumptions.

The issue is not "newbies". The issue is newbies who refuse to do anything
about their lack of background while continuing to spout nonsense.

Even a newbie should know basic secondary school level algebra.
One can't discuss a subject without knowing the basic language.

Yet, we had a newbie who didn't even know the difference between 2*x
and x^2.

I am totally ignorant about many subjects. For example, even though I know
quite a bit of math (and can handle tensors etc.) I am a newbie when it
comes to Quantum Field Theory. The subject fascinates me. Yet, I recognize
that should I want to attempt to make a contribution, I would need to put
in quite a bit of studying. I therefore do not presume to make "suggestions"
or put forth "it seems to me that..." statements to quantum physicists.

I do not think it unreasonable that we demand that anyone wanting to
discuss Mersenne Prime Testing understand basic algebra and basic modular
arithmetic.

[T.Rex]

Originally Posted by Numbers

... you will see that it (LLT) can also be used for other primes ...

In his famous book (A little book for bigger primes), P. Ribenboim creates some confusing situation because the theorems he provides about Lucas Sequences are limited to N-1 numbers, though this theory can be used for N+1 numbers like Fermat numbers. I have'nt checked in William's book, but I'm sure Williams provides the full theorems. I've talked about that in the 2 papers: Two Primality tests for Fermat numbers based on Lucas Sequences and A LLT-like test for proving the primality of Fermat numbers .
Regards,
Tony

[trilliwig]

Originally Posted by mfgoode

I tried but did not get the formula in question
Mally

http://en.wikipedia.org/wiki/Lucas_sequence



Deriving the relationships are a fun exercise in induction.

[cheesehead]

Originally Posted by R.D. Silverman

The issue is not "newbies". The issue is newbies who refuse to do anything about their lack of background while continuing to spout nonsense.

No, that's not the issue, either. We've discussed this before.

we had a newbie who didn't even know the difference between 2*x and x^2.

Correction: We had a newbie who confused x^2 with 2*x in some formulas for a while, perhaps through misreading, but who, when he finally recognized what we told him was his mistake, had no trouble knowing the difference.

I do not think it unreasonable that we demand that anyone wanting to discuss Mersenne Prime Testing understand basic algebra and basic modular arithmetic.

(* sigh *) We've also discussed that before. I think it is unreasonable to demand that posters in a public forum who have satisfied the criteria (i.e., registration) about which they were informed prior to their postings are necessarily to be expected to satisfy additional criteria just because some experts are unable to restrain themselves from responding to certain postings even though those experts have been previously informed of criteria by which they can determine when their demonstrated abilities are a poor match for that category of posting.

[Orgasmic Troll]

Originally Posted by R.D. Silverman

The issue is not "newbies". The issue is newbies who refuse to do anything
about their lack of background while continuing to spout nonsense.

Even a newbie should know basic secondary school level algebra.
One can't discuss a subject without knowing the basic language.

Yet, we had a newbie who didn't even know the difference between 2*x
and x^2.

I am totally ignorant about many subjects. For example, even though I know
quite a bit of math (and can handle tensors etc.) I am a newbie when it
comes to Quantum Field Theory. The subject fascinates me. Yet, I recognize
that should I want to attempt to make a contribution, I would need to put
in quite a bit of studying. I therefore do not presume to make "suggestions"
or put forth "it seems to me that..." statements to quantum physicists.

I do not think it unreasonable that we demand that anyone wanting to
discuss Mersenne Prime Testing understand basic algebra and basic modular
arithmetic.

I'm stepping out on a limb here, but I'm inclined to believe that someone who is an expert in one field is more likely to have a keen awareness of their ignorance in other fields. I think you may take for granted your understanding of your own limitations, expecting the same from others who have not yet gained that level of self-awareness.

Speaking from my own experience, I was a math newbie who had more enthusiasm than good sense and made my own stupid pitfalls. Unfortunately, up until very recently, I have had little to no contact with the mathematical community; I surpassed the mathematical abilities of everyone in my family and my circle of friends when I took trig. As a product of the ever-faltering public school system, there was no one to foster my talent, no mentors, no one encouraging me to pursue it further. In my spare time, I read math books written at a level for public consumption because I didn't have any resources to help decode the cryptic language that more rigorous books are written in. Honestly, I feel cheated. I was probably around 11 or 12 when I found out about imaginary numbers, and thought to myself, "hey, so does make the number line into a number plane?" I asked my math teachers every year if it did, and they all gave me blank stares. It wasn't until Algebra II, where we actually used that idea, that the teacher had any idea what I was talking about. I had no one with which to share my enthusiasm for math, no encouragement to pursue it further, and no idea what was beyond high school math, so I ended up pursuing one of my other talents and went to art school for 2 years before realizing that I can live without art, I cannot live without math.

Upon transferring to a junior college to effectively start my college career over from scratch, the situation wasn't much better than high school. There were no upper-division classes, and so I was trying to teach myself modern algebra from the Dover book. Asking my calculus III teacher about modern algebra, she admitted to the class that she had absolutely no understanding of it, barely made it through the class in college and she couldn't even remember what rings, groups and fields were (her exact words were, "if you ask me about rings, those go on your finger. Fields? That's what you play soccer on.") Last semester I finally finished my time at community college and took an Intro to Formal Math class at a local state college. Without one iota of conceit, I was a big fish in a little pond; I was head-and-shoulders above my peers in ability and enthusiasm for the subject (I start this quarter at a UC, I hope the disparity will vanish)

My apologies for the long-winded autobiography, but my point is that there are many people out there with similar experiences who simply have no idea what they don't know. That doesn't make answering their questions any less annoying, and I fear the karmic backlash waiting around the corner for all the stupid notions I've thrust upon the mathematical community, but it's not unreasonable to ask for a little understanding; "Forgive us, for we know not what we do"