h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I briefly looked at your work on prime sequences. I wouldn't call it numerology although it does look a trifle arcane (it IS a proposition based solely on base-10 arithmetic). I suppose such propositions have their merit. Didn't Cantor or somebody construct a transcendental number using base-10 arithmetic? Do you think you can make your work of interest to the layman?

P.S. I sent the multiple-word C programs. There is a considerable amount of software associated with most of the Guide Entries that I've written. I'll send you that software as well if you're interested.

I should be clear that I don't regard myself as a mathematician of any merit either. If you are ever in need of a good program for factorization, the link http://www.alpertron.com.ar/ECM.HTM is good as a tool, allows access to the source code, and explains some of what it is about. I really only know it appears to be the best tool around for factorization. Primality testing and factorization rely on different algorithms and this tool is not supposed to be anywhere near ideal for just primality testing. With the right tool and good programming around it, I'm fairly certain the fifth term (at least) of the sequence I'm researching to find the fourth would probably be a piece of cake. Its companion sequence will be a challenge for someone to advance (with proof) any further than it already is since it is about primes being anywhere in the sequence and the numbers get very large.

Yes, the 4CT article is good. I tried to get the author to consider adding some things, but in retrospect it is just fine for h2g2. I just replaced my old PC and got back on the internet after a long hiatus before which I was only playing games (chess and reversi). PlanetMath is new to me. I found this site through its mention on wikipedia after fighting the people over there about original content that I argued with no success was not really research but in fact more-or-less dropped in my lap.

I'll get back to you about what I think of your work and whether the specific Entry seems like a good candidate for the Edited Guide around Tuesday. This scanning process I'm doing should be done by mid-day tomorrow, and then a few other tasks are also on the agenda.

I will definitely be taking some interest in the various discussions about the 3n+1 problem. Even though it's not any closer to actual resolution than when I was younger, it's a different problem than it was then.

If you have any questions about my coincidences, give me a shout here. If you want I can let you know if discussion of them shows up in real time again. Right now it looks like nobody wants to know about it, since my phone number has been revealed as part of it and nobody has checked my veracity on this even.

I'm not sure who did the transcendental number stuff you are thinking of (or necessarily what you are thinking of), but I'll be sure to address that from my library next week. Aside from what I mentioned already, I am having my computer run the applet just referred to in a search for a prime in base seven analogous to 82818079...987654321 (Another rediscovery of mine, this is the only prime of its type up to leading part in the 30000's--I only verified to 1000 before I took it to wikipedia's help desk).

Oh, well, if it's no bother to send it, please do.

The following link should send you to the discussion between myself and PrimeHunter. I should not have been so lazy that I did not provide this in my first posting.

http://en.wikipedia.org/wiki/User_talk:PrimeHunter#New_Prime_Discovered

Say, that is a good website. The elliptic curve technique is what I saw in Mollin's book on algebraic number theory. Thanks. I see you're way ahead of me on factorization; the C programs I sent you are probably of no use to you. If you get interested in the 3n+1 problem and least-residue trees, then they will be of use. There aren't any really good non-technical websites on the 3n+1 problem that I've found. Oh, there are websites that collect statistics on really huge numbers in the sequence, but I don't consider that to be very productive. Lagarias appears to be the technical guru and there's Gunther Wirsching's book (which is hard to read).

You're welcome, but keep in mind that it may not be ideal for primality testing if you're ever into it (Mr. Alpern updates frequently, though, so I might guess he'll improve that part); and thanks for the programs which I'll make something out of in the way indicated. I really hardly remember what C I learned, and it may be a good starting point to just read the writing of some of your programs.

I'm generally not going to devote a lot of time to problems that are hard and overworked relative to the likelihood of their being resolved, but I won't know if that's the case with 3n+1 until I dig into it a bit. I might end up taking a great interest, dropping the subject, or something in between. We'll see. Most likely, unless I have some wild insight into how to prove common wisdom correct, I'll probably just get up to a basic level in what other people are doing and then drop it altogether for twenty years. I've heard of Lagarias.
I don't recall hearing of Wirsching before, but his book may be something to order.

I looked at your conversation with PrimeHunter; there is a lot to be researched there and you must have done considerable work to get set up with the software. I have to admit that this type of work is not my cup of tea; it's too far from mainstream mathematics and too close to recreational mathematics. But, then again, I didn't think there could be anything interesting about the 3n+1 problem when I first saw it. I agree with the professional mathematicians; it's hard and no amateur is going to solve it. (It tickles me when newbies complain that there is no structure they can get a handle on. There's lots of structure; you just have to know how to look at it.)

smallfrey:
Nothing about the set up was difficult or time-consuming, actually. The part that was time-consuming I could have instructed an eight-year-old to do rather quickly, if I had had one around. PrimeHunter also didn't have to work very hard to do what he did, but he's an expert mathematical programmer in the field.

Well, I'm glad you have realistic expectations with the 3n+1 problem. I'll just find out what people are saying about it in enough detail to get a handle on whether any insights have slipped through the cracks somehow.

I didn't think of the subject I inquired about as anything other than recreational mathematics, but I thought you might take interest in it as a special kind of that. No rush to get results really, and I need to learn to really program for other related things anyway, so there is no problem.

I will continue now with what I'm doing and do as I said I was going to do on Tuesday.

If you do read any of my articles, here's what I consider to be the best; (1) "A Unified Approach to the 3n+1 and 3n-1 Problems", (2) "Fermat's Last Theorem and Related Problems", (3) "A Partitioning of the Natural Numbers 1, 2, 3, ..., Q-1 into N Sets where Q is a Prime, N Divides Q-1", (4) "Necessary and Sufficient Conditions for a Nth Degree Mod P Congruence to Have N Roots", (5) "The Cross-Ratio Function", (6) "Farey Series", (7) "Fermat's Congruence Modulo a Prime Power", (8) "An Interleaving Technique", and (9) "An Algorithm for Computing the Determinant of MxM Circulant Matrices where M is a Power of Two". Some of the articles would have been good 18th or 19th century mathematics.

You'll be the first (sorry that I didn't do a very good job of reciprocating). Some possibilities are; (1) nobody's interested, or (2) somebody's interested, but the articles are far beyond their poor power to add or detract, or (3) somebody's interested, but they hold these truths to be self-evident, or (4) somebody's interested, but they think it's all a bunch of crap.

I just woke up, and I'll be reading promptly. Pretty much done with what all else I had to do.

I will comment on each article in turn in a seperate conversation for each. I'm starting with your Generalized Smarandache Function in a trice, and then I will take the articles in the order mentioned. The first thing I'll do for each is comment on whether the content of each subject seems okay for the EG. Slow getting started tonight. I didn't go right to it and I had forgotten there was a baseball game.

I decided to stop for the day with the comments and look at your entire collection before saying anything else to a single article. What are you doing writing this at h2g2? You're right about this not being the proper venue for serious mathematics. It seems you made a mistake there by not looking at other articles already edited.

Yes, I did make a mistake by not taking the other Guide Entries more seriously. I looked at the h2g2 charter and didn't see anything prohibiting non-elementary articles. Only when I tried to do an Edited Guide Entry did I find out that the articles were supposed to be geared to the level of 12 year olds. Still, I thought that if I gave the prerequisites for reading the articles in the introductions, somebody might read them.

It's no big loss; I entertain myself by writing. My articles are not suitable for the other end of the spectrum (the mathematical journals) because they contain so many empirically derived propositions. The Fibonacci Quarterly expressed some interest in accepting the article on "super" Fibonacci numbers ("Necessary and Sufficient Conditions for a Nth Degree Mod P Congruence to Have N Roots"), but they wanted me to re-write it using Latex. I used to know Latex, but I've forgotten it (thankfully).

Are you planning to try grad school, or is your position to work independently and leap frog to mathematical fame somehow? Clearly, you could get through grad school just about anywhere at this point in about two-and-a-half years maximum.

It's too late for me; I'm in my early sixties and my brain cells are dying off faster than I can replenish them. A lot of the articles are work I did 40 years ago (I had to take a break from mathematics to deal with the real world). Besides, I don't have any delusions about what my capabilites are; I'm just a dabbler. I'll be satisfied if I can impart some of the things I've learned to at least somebody.

Ooh! Well, you're modesty is heavier than it need be, to say the least. I apologize for any discomfort about what might have been I may have caused, but I will say that there is little doubt in my mind that some of what you work on could find a place in "The Journal of Computational Mathematics" (I'm not expert or affiliated with the journal, keep in mind). You might take a look at the articles there some time to see if you want to try. I totally misjudged your age to start with. You would be extremely advanced in mathematics for the age I thought you were originally, and still very advanced for what I thought after your Lenstra remark. You do good work, sir, and I will try to get all I can out of it.

Okay, the humility is false; I'm a good dabbler. I sent you a "WinZip" file containing C programs that you might find useful.

Okay, I see you are done with the subject then. I will begin getting into it (outside of just collecting material) at the beginning of next month. I'm going to go through the 2002 edition of Stewart and Tall (ANT and FLT) with a fine-tooth comb along with getting the detailed contents of all of your written work here from said work and my library this month. If that doesn't leave time for much else, I won't do much else. Today has been a bit of a fiasco (with people insulting each other and some real content) here on hootoo. The rest of the night (for me, that's till 4AM my time) and tomorrow, I don't need to engage in it; so I will be getting further into your articles without allowing myself to get distracted.

I got your programming stuff and the remark that you think you are done with 3n+1. I'll open and get through what I can at a reasonable pace for me. I will immediately (tomorrow) schedule in some of your programming at a pace of one hour per day. I have a compiler.

Some things here at hootoo maintain my interest. I opened two discussion streams under "ask h2g2" and one under "miscellaneous chat", and I'm also doing some Peer Review on science matters. This is a very contentious place, and it has such a vast mix of intellects.

I'm still not done reading your articles, sorry to say, but you can expect more of my thoughts in one long post here (and the other conversations I started, possibly) during the next week.