## JSH: Some important info on prime numbers

Some of the arguing about prime numbers that I'm facing may be about not understanding a few basic things about the known and accepted theory on them, so I'll give a quick post to go over that broadly as it is a fascinating subject. I'm going from memory here so if there are errors, sorry, and others may correct.

First off, it was Euler's zeta function.

Mathematicians had noticed that the count of prime numbers aka the prime distribution was related to these continuous functions and Euler found this cool power series that allowed him to find limits. But it was HIS zeta function and NOT Riemann's. Riemann later took Euler's zeta function and did a few things which I'll come back to in a bit.

Chebyshev actually did some great work refining the limits with Euler's zeta function, and his work later became called the prime number theorem for some reason or other, and others have done a lot in that area.

Now Riemann came along later and trying to answer the 'why' of the prime distribution he got creative and pushed Euler's zeta function beyond an asymptotic area with analytic continuation which was a clever way to go into the complex plane into the "imaginary" numbers area.

I've had to think on these areas because of my own prime counting function, which gives a 'why' of the prime distribution by connecting prime counting itself directly to a continuous function through a partial differential equation, which means that my idea could resolve the Riemann Hypothesis directly.

Gauss was interested in primes as well, of course, and did his own work in this area including introducing the Li(x) function. But it wasn't until after he died that twin primes became a big deal and the twin primes conjecture hit the stage in the late 1800's.

There are two things that happen with the twin primes conjecture and prime gaps:
1. There are empirical formulas based on the actual gaps which tend to include x/ln x or Li(x), which I say is wrapping up the prime distribution with that count, and they often have components that fit with the probabilistic approach I have. They have values that are corrected using actual data, like for a constant called c.

2. There are bounds given usually through something or other related to the Riemann Hypothesis which are more in the area of derived as ultimately they trace back to Euler's zeta function which has known reasons for being connected to the prime distribution.
My own position is that the probabilistic explanation is THE explanation and that the prime distribution itself is falsely correlated by many math people with the prime gaps as you can just throw it away, and get the answer by considering the number of primes within a particular interval with a probability calculation.

My idea greatly simplifies the area, and dismisses the need for any other explanation, resolving the Twin Primes conjecture with a probabilistic explanation which may be unsatisfying, but worse, the same idea allows you to disprove Goldbach's conjecture which is even more unsatisfying as that proof—or what I think is a proof, kind of hope it's wrong—indicates that a counter-example has such a very low probability that it is unlikely to ever be seen.

Oh, my prime counting function for various reasons also makes it seem likely to me that the Riemann Hypothesis is false, which of course really upsets quite a few apple-carts as established math society opinion has been that it is true.

And that is a quick overview! My research gives a why for the prime distribution, why it is connected to continuous functions like x/ln x, and the why of prime gaps. It also gives a direct path to resolving the Riemann Hypothesis, which I think is false. But it also resolves the Twin Primes Conjecture and Goldbach's Conjecture, but in what is probably an unsatisfying way.

I highly recommend interested readers dig into the history and learn more about Euler's work with his zeta function. Understand how it relates to the prime distribution and learn who Chebyshev was as well as why Gauss came up with Li(x).

It's a fascinating story, and Riemann isn't the only interesting player. But he also was actually working on getting an answer to a problem I answered, so, it's kind of one of those odd things for me talking about him.

Oh, but it IS a fascinating thing to consider that mathematicians might not want the correct answer here, as my research as a way to resolve the Riemann hypothesis has been out there for years.

My suspicion is that for mathematicians whose lives have been turned upside down by my research findings, it's just one more log to toss on the fire which is burning away their research like it was, well, trash, and knowing that I'm probably right is just something they can run away from like they do with the rest of my research.

But why does the world let them? A question for historians, social scientists, and other scholars.

## JSH: A very uneducated culture?

You know I just got through with some exchanges that were maybe heated a bit but not terribly more than normal, and the issue of probability and statistics has come up in my threads, and it occurs to me: how badly educated IS our modern culture?

How many people are there out there who think they understand issues like global warming but have no clue about the math?

They think they know, but they see a cold day in the summer and go to themselves, Hah!

Does Usenet maybe make it worse for some of them, by giving them the illusion that they're engaging in rational discourse even if they're painfully inept at it? How aware ARE posters in these math areas when they stumble mightily and show complete ignorance?

YES! I know many of you wish to say that's me! Ok then, use me as an example I don't care.

How big is it as an issue how uneducated our culture is when people are "loud and proud" and really to yell to the world their opinion on just about any issue?

For math relevance (it is a math newsgroup of course) to what extent are arguments on the sci.math newsgroup driven by a horrible understanding of the mathematics, as in pathetic to the point of absurd? Almost as if the person yollering knows next to no valid mathematics AT ALL?

## JSH: We must move on

As required I am making my public statement so that the human race has its notice.

They have reached their limits Mother. There is no point in continuing these tests!!!

They have failed. They had their time and have done as best as they can.

It is time to move on.

This demonstration should end.

I have fulfilled all obligations. As required the species has been given its chances. This world has made its will known.

Evolution has final say. So I'll await Her judgment, but I have done all that is necessary.

It is time for the next phase.

## JSH: Prime gap equation, 3 years grace

Posters like to attack my prime residue axiom by picking on a single prime, like claiming that p mod 3 does show some kind of regularity, like today I saw a post saying 1 follows 2 or 2 follows 1 as a residue or something of that nature, when the full axiom covers ALL EVEN PRIME GAPS which leads to the prime gap equation. And I've noted there is only one.

So the prime gap equation can be programmed, and used against all prime gaps out to millions upon millions of primes.

That test I'm sure will end all rational debate.

It is a test I have said I would not do for at least three years and I think I said that about a year ago, so there are around two years grace left for the mathematical and physics community as my results have implications for group theory as well.

To end the grace period some dumbass would have to claim a twin primes conjecture proof and get credited for it, or claim a Goldbach's conjecture proof and get credit, and then I've said I could just go ahead and kill that noise by doing the above.

So the math committees won't do it, I'm sure. So it's like you're wasting your time to try. No matter what "proof" you may think you have, you'll get shot down faster than Goldstone did (of course he was shot down before I ever said I wouldn't allow it).

(The math error allows a "proof" of just about anything. So there may be people who have to be blocked by the math committee when they put forward an argument correct by the established mathematical ideas.)

Which raises the question, if I can end the debate, why not just do it immediately?

Well, if I do it, I'm certain there would still be a lot of arguing, and a lot more ignoring. It'd be an uphill climb with lots of denial, where I'd be pushing people against a wall. That's not safe for ME to do. Some of you may notice that I put things out there for others to do, as I think there's safety in numbers.

And it's weird to me that there is the prime gap equation hanging out there. Which means there are these people going about their lives with this thing hanging over their heads. And it's curious that they would do so, but hey, you do what you feel like you have to do…

Real world is a nasty place. It's competitive, and it's not some fictional story. People clash and fight over all kinds of things and it can get REALLY nasty. To most of you none of that matters as you're not important enough for it to matter. What you say on Usenet is as worthless as what you do in your daily lives. You CAN say anything. Few people, if any, actually care.

But I'm one guy. I push math people just so far. And then I back down. Which has been going on for years, as I know that when it gets too nasty then people can get physical. So there is a three year grace which could be extended. Years can go by, and I've noted I'm getting comfortable with 2030 as I ponder this situation and see a math community that is settled into error at such a depth that more than likely, yes, things would get physically violent if I pushed too hard.

That the human species will allow itself to be paused for that long could be about destiny.

Truth can be too expensive you see. And at the end of the day, ignorance is the natural human condition for most. And it doesn't seem to keep them from doing the most important thing they do: reproduce.

As long as people keep making babies, it doesn't matter much if their math is wrong.

## JSH: Some history

It has been about two years since I noticed that some of my research I call surrogate factoring lead to a method for solving k^2 = q mod p, and what happened back when I did notice that and also still thought I had a good approach with my surrogate factoring is I promptly left it to think about the Traveling Salesman Problem. And I thought up this idea of having the traveling salesman going backwards in time to meet himself. So THAT idea is now two years old as well.

And then I did other things.

I'd talk about things related but I was actually scared of both results for different reasons, many of which I've given before so no reason to rehash them here. But eventually I came back to surrogate factoring and decided one group of equations didn't work that well after all, so focused on the part that could solve k^2 = q mod p, generalized it November of last year, and finally, belatedly this year generalized it fully to consider k^m = q mod N.

And I sent a paper to the Annals of Mathematics, got antsy and decided to post about it, to see what that might dredge up—maybe someone could thankfully clobber the result, kill it, dead—and I got the usual crap, but then someone mentioned discrete logarithms—the "Mark Murray" poster—and next thing you know I've figured out a way this approach can handle discrete logarithms and got really scared again.

Now with time and distance I'm calmer so yes, this iteration of posting is almost over. But I think posters who see a static situation here where I just do the same thing over and over again are in a strange fantasy world of their own, as I've progressed over multiple lines of research, and quite often taken long breaks from a particular line for various reasons, including when it terrified me.

These results terrify me.

I have no problem with wandering off for YEARS, and am in the process of doing just that, while the paper at the Annals may offer a chance of something happening, I've dealt with them before, and see them as being as corrupt as the rest of modern math society so no major expectations.

So nothing more from me should be expected on this subject, possibly for years.

If that comforts you, fine. If you think it's a great thing. Ok. But if these results can be developed, then I'm not doing it.

I'm running away from them. Fast.

And that is what this post is about: me running away. So in a sense the heart of the k^m = q mod N result is about 2 years old. I could probably have had the result 2 years ago. I didn't want it then and I don't want it now. But if I have it, others have it, and probably HAVE had it, for maybe 2 years.

So posters can reply as they will. I've posted longer this time as for me posting in a public forum gives me the sense that hey, at least I can still post! And that tells me things. I'm also the one who is often dragging his feet and I leave all kinds of research up in the air, as I have so much anyway, and a lot of it, terrifies me.

But it looks like I can just walk away here. So will walk away, can stop posting, and wander off to do other things. It seems to me that it is possible that the full general result is two years old anyway, as if someone were following me, they could generalize easily, so if it HAS been developed, it doesn't need my input any more anyway, as I'd be two years behind, and it doesn't matter as I'm not DOING ANYTHING ELSE any way.

I emphasize that I'm no longer working in this area. It is on the back-burner like so many other results.

I am walking away.

## JSH: So what happened?

To people today Gauss is a name, of a person who lived a long time ago, and they're told he did great things. But to his contemporaries he was the one to beat. The best of his times. When he died the push to find something great lead a world astray.

With him gone, the mathematicians of his time could go astray.

Prime numbers have no preference. To consider all twin primes up to 25, you only need 3, as 3 commands them.

5 mod 3 = 2 so there must be a twin prime. But 7 mod 3 = 1, so there cannot be. Because 9 has 3 as a factor.

For 11, you have 11 mod 3 = 2, so you have a twin prime. But 13 mod 3 = 1, so no twin prime.

17 mod 3 = 2, so a twin prime. But 19 mod 3 = 1, so none.

And 23 mod 3 = 2, but finally 5 steps up, so no twin prime.

Then 3 and 5 command all twin primes until 49.

It is trivial. It was always trivial.

But if you believe that it's not trivial, then you can wrap up the prime distribution itself. The count of primes up to 25 is approximately 25/ln 25 and you can put that into it and make this complicated thing, and say you're doing great things and pretend to be like Gauss.

I've asked, why do math research?

None of you know why. You don't know why because if you did then you would not believe in wrong things. You would not hold so desperately on false beliefs, false hopes, false dreams.

Because out of what is wrong comes not the strength of the human race. What you build upon the lies will not stand. What you do with the praise of people who believe in you wrongly, will not take you far.

Your world changes beneath you. As it shifts you hold on desperately as if you can comfort each other with words then you believe you can keep going if only for just one more day, as you remember the previous day and that seemed to work.

But this world is about actions and your warnings are nearly done. Few of you have a clue of the world that is coming no more than you knew this one today would be here, and your warnings are about your physical safety but I know for some of you such warnings mean nothing as you are past caring about dying.

I have done my best. But you must understand that for many of you this story may end in a very short time, less than a few years in your fellow human beings exacting a steep price upon you.

I will try to save you as I can. At least some of you. What you have not understood is that Evolution is about survival.

And surviving is about being right. For some of you soon, I will be the only thing keeping you from death.

We are nearly there.

## JSH: Why do math research?

I use Usenet to brainstorm and in this cycle have wondered at times myself, what am I working on exactly now? And it occurs to me that I'm moving to what I think is a meta problem which is the global question of: why would anyone do mathematical research?

And anyone can.

I've repeatedly noted that I'm not a mathematician. And I do admittedly amateur math research for complex reasons and having come up with various explanations over the years, I've decided that a key one is that I ENJOY my little scribblings on lots of paper, and talking about them even in areas where a lot of people are mean to me, as I don't have any other places.

Rather than not talk about my math unless I can get feedback without nastiness as well, I have had to try and learn how to deal with the nastiness, and stay focused on the why of posting itself, which I do. I use Usenet.

So then, why should anyone do mathematical research? And can anyone do it? Do modern professional practitioners sufficiently hold the door open to outsiders? Or do they try to hold it closed claiming only they do it best? Do they do it best?

## JSH: Why of prime gaps

Recently an idea I had several years ago about prime numbers seemed to me to be actually an axiom about prime numbers themselves, which was rather exciting and I suggest that it is surprising that the world has either yawned or is not aware of how significant it is, but it among other things quite simply explains the why of prime gaps. In this post I'll quickly show how that is the case by focusing on the twin primes.

An example of twin primes is: 11, 13

The gap between them is exactly 2, and one way of looking at "why" is to note that if for any odd prime p less than sqrt(11), if (11+2) mod p is 0, then the prime gap can't occur. May seem trivial but it is the key to understanding the twin prime gap.

For instance look at 13, where the next prime is 17. That's because (13+2) mod 3 = 0.

That's it. It's the only reason. Mathematically THERE IS NO OTHER.

But also notice it means that 13 mod 3 = 1 is needed. So if 13 didn't allow itself to have 1 as a residue modulo lesser primes then that would have been a second twin primes case, but that is ludicrous. How could the prime 13 decide that it doesn't like a particular residue mod 3?

And that's your clue. If you understand that one thing then you can grasp the why of twin primes and then of arbitrary even prime gaps, as for instance for that gap of 4 between 13 and 17, you needed (13+4) mod p, where p is an odd prime less than sqrt(13) to not be 0, for, once again 3.

Mathematics doesn't need anything else to say a prime gap is there! There is ONLY one way to get a prime gap, which is for

(p_1 + g) mod p_2

to NOT be 0 for any odd primes less than sqrt(p_1). If it is, then that gap does NOT occur.

So the requirement is that p_1 NOT equal -g mod p_2, for all primes p_2 less than sqrt(p_1).

If no residues are excluded or preferred by the primes then there will always be cases where those conditions are met, which trivially proves the Twin Primes Conjecture.

(Think carefully and now you can disprove Goldbach's Conjecture trivially as well, but without a counterexample likely to ever be directly seen which is unsatisfying I admit.)

Another way of looking at it is, if you're looking at bigger and bigger primes p_1, and you are getting all these residues modulo primes less than sqrt(p_1), and there is no preference by the primes then just at random at times you will have cases where -g is not a residue modulo ANY of those primes which will give you a prime gap.

(Primes may here define random for the real world.)

So those go out to infinity.

What's interesting about this issue may be that people rarely talk about the why of prime gaps so it seems like a hard problem, especially if you wrap the prime distribution into it which you can do with a false correlation. That is, as the count of primes drops as you get bigger numbers, necessarily the count of twin primes will drop as well, but the prime distribution itself is irrelevant as to the reason of the "why" of twin primes or other prime gaps.

## JSH: Some math history

After Gauss died in the mid-1800's, other mathematicians attempted to take up his mantle in various areas of number theory, and a lot of issues I'm currently discussing trace back to that period so it's worth a quick bit of math history, and I like to start with Riemann.

Riemann decided to solve a bit of a mystery that had fascinated mathematicians including Gauss which was the apparent connection between the count of prime number aka the prime distribution and x/ln x, and Li(x) which Gauss contributed. Gauss hadn't figured it out and the so-called prime number theory was not yet considered proven. Though Chebyshev among others had done significant work, with Chebyshev doing some really great work around Euler's zeta function.

(See: http://en.wikipedia.org/wiki/Prime_number_theorem)

Riemann came in trying to figure out the great puzzle and did his own work with the zeta function, and he came up also with his tangential famous hypothesis, but I solved the question much later with my prime counting function by using a P(x,y) function which had a partial difference equation, as I could then casually walk it over to the calculus with a partial differential equation.

Along with the prime distribution itself, questions were raised about the twin primes distribution, and some complicated research emerged, which I've shown was about a false correlation as because the count of primes drops the count of twin primes drops as well, so those mathematicians thought they were intimately connected mathematically, while my prime residue axiom shows that it is incidental connection.

That simplification allows a prime gap equation and the consideration of arbitrary even prime gaps.

My research simplifies huge swaths of number theory. And simplification probably would have been heralded—back in the late 1800's. But today complexity pays the bills for a lot of math people.

So today there is an impasse. Like the mathematical researchers before me I kind of just pile on the results! Which makes it all the more fascinating watching the modern math community ignore them!

But it is enlightening for governments and various institutions.

Oh, the Riemann hypothesis is most likely shot down by my partial differential that follows from the multi-dimensional prime counting function which is a guess that is supported by that attempt to ignore it all by the modern math community as it has a position that it is probably true. If my research supported that position then it seems unlikely that math people would continue to brazenly ignore my P(x,y) prime counting function.

So that's a little historical perspective. It's not clear what will happen to end the impasse but historically these impasses usually end when the old guard dies off. As new students come into mathematics having heard of my ideas—that's why search results are so important—they won't be so invested in the old stuff.

Which is the time line. As kids move into college, they'll probably bring some knowledge of my research. The old guard will probably fight that as hard as they can but historical perspectives say they will eventually fail.

Until then, I get to argue on Usenet and do other things. It's kind of a pass for me, as I'm still too young to be a world figure.

One guess is that the world is taking care of me in this stage. Allowing me to mature, and age. I need to be maybe a decade older to handle this situation gracefully if there is any chance I will.

I may not. I'm just not the old kind of discoverer. I'm 21st century.

So I'm more than a little nutty. A lot more than a little wild. And not really happy with this freaking role anyway, as I try to figure out the best ways to work it.

Maybe it's better when I'm 60? So maybe a couple of decades? By then much of the old guard will have retired out of the math field. And I'll have had lots of fun and could possibly be that old wise geezer the world would probably prefer.

So we're aiming for 2 decades at this point. Or the year 2030.

## JSH: They lie a lot

I used to get upset but now I find it just to be an odd lesson in human group dynamics when some poster or posters say something really mathematically wrong and other posters try to post support for them, when I jump on it.

(I like jumping with both feet and hitting as hard as I can when I get in the mood.)

It's so predictable. And it's so odd. It IS mathematics. It's not like the results will change.

And who cares really? So some Usenet posters get basic math facts wrong, why should other posters jump to their defense with so much gusto? Do they feel sorry for them? What? I find it somewhat puzzling as I'm not sure what they think they accomplish.

Will math people start believing that a prime gap equation already is accepted? No. Will they think better of the posters who screwed up? No. Will I accept their defense? No.

Will anyone really care? Probably not.

I think there are about a dozen posters who see themselves as like a gang, so they stand up for each other.

And they don't seem to care how obvious it is when they are wrong!

So at times like these I kind of settle in for batting practice, as I just kind of keep whacking for a while, as you will see in the threads, which is also why I tend then to put up more threads!!!

More opportunities to practice knocking them out of the park. Practice is important to give you that edge.

I like my edge.

It can get boring but I think practice is a good thing.

After all, in these situations, these are slow pitches to a home-run hitter.

## JSH: Maybe they're fakes?

I've wondered for years if maybe there are people who've been hired to argue with me, who are trained in psychological operations and not mathematics.

My latest trick with prime gaps snared them nicely, if so, and now I'm curious what techniques they will use.

I STUDY those techniques.

## Understanding prime gaps issue

Even a novice math student SHOULD know that the world does not supposedly have a prime gap equation as with one you could prove or disprove the Twin Primes Conjecture as well as an infinity of conjectures of that type.

So my claim of having the world's only prime gap equation is a fascinating one.

Someone with basic math knowledge who thinks I'm full of crap would just reject it outright as a false statement.

My own claim follows from my prime residue axiom, and is tantamount to a claim of having proven the Twin Primes Conjecture.

Search in Google: prime gap equation

## JSH: Trying to be fair

I point out how I use Usenet as I think it's the right thing to do. Posters may order me to behave a certain way and I'm not going to do it. But at least I can let you know what my methodology is. And yes, insults do fly at times, but I get insulted a lot, and I insult back, or I don't. But I also am dealing with what I can prove is the recalcitrance of people who have broken their own rules, refused published proof—killing a mathematical journal no less—who are relying on flawed math for their livelihoods, or for their delusions of value in their own "research".

Social structures can be powerful.

It doesn't mean they are right about mathematics.

Time is the best judge.

As time has gone by I've been privileged to watch new technologies render hostiles who inflict verbal abuse upon me—shift it to Google, as they proclaim Google search results mean nothing.

Why? Because I've seen my research rise in Google search results, and rise in search results across search engines, so for them, there is no choice, I guess. You might think the truth is a choice. I thought so too but then again, years ago I thought all kinds of things before learning better.

People can quite deliberately choose to be wrong. And ignore all evidence.

I try to be fair. I have the best seat in the house. For me it is a world away from where I was years ago arguing on this newsgroup, wondering if I'd ever find anything valuable. Hurting from my failures, questioning myself, wondering why I bothered, or couldn't just stop. Wondering why there were people who wanted to say so many nasty things to me—night and day, day and night.

Then it got harder. I didn't ask the ring of algebraic integers to dispute the field of complex numbers. It did so before I was born. It can't help doing so, it will do so until the end of time. To me, the refusal to accept that is so much about how our world can have so many problems that are solvable as people who are invested in being wrong do not care about the correct answer.

If mathematicians can sit back, and keep doing what they're doing when it's EASY to show a deep error, and an astounding conflict between ideas, then there is no puzzle about how people in harder areas to find truth can do so many of the things they do.

The truth will not change.

There is a sadness though when you see people who have invested so much in error when it wasn't their fault, who decide that they'd rather be wrong when the error is revealed—they did not know before but how can they continue in error after?—and I'm not the best person though to appreciate that feeling as of course I can say the above knowing that my job was to show that error. Knowing that I get to be right.

So I get to be the lucky guy, right? So lucky. Petty arguments don't change much for me.

But what I can do is warn you. There is no reason to argue with me to make your place in history as one of my foils. I have a method that I've used for years. It is honed by years of practice.

Denial of that reality does not change what happens.

It merely give me more people willing to work to insult me for a while, but work them I do. I think a lot of them actually don't do a bad job. But at the same time to be fair I need it out there so this message is like so many before explaining that I use Usenet.

You have been told yet again.

## JSH: There is only one

Oh yeah, there are areas where I have the world's only of something, and one such area is with prime gaps.

I have given the world's only prime gap equation.

There is only one.

Remarkably to me math people can be bizarre about their insistence on ignoring even dramatic mathematical discoveries—from people like me.

But it doesn't matter. Soon enough they will be dust, and their petty behavior fodder for history to ponder. Their own "research" long forgotten as so much of it is useless, or they probably wouldn't be so stupidly petty as they are today.

Only those with value can see value. Only those who have found value appreciate value.

So they are an odd point in history, which will pass.

Yet my prime gap equation will still be the world's only.

You see, there is only one.

## JSH: To my Chinese fans—thanks!!!

There has been a cool new reality to me of getting more positive support than in years past, from people writing Chinese. And I wanted to do a shout-out of thanks to my Chinese fans, hoping that this post will loop around the world like most of them do, so that they will see it, and sorry that I can't put it out in Chinese.

It does occur to me that an oddity of English speaking angry people ripping on my ideas night and day would be that those ideas would travel best in areas where that does not occur. And I think also that while I may have people interested in my work who speak English as well as Chinese, they probably are aware of the hostility from the English side so are safely sticking with Chinese.

I think that's a good idea.

It's best for people interested in my mathematical research who speak languages other than English to stick to those languages to stay away from the vitriol, angry hostility, and quite simply, rage of English speakers directed against my research and me.

## JSH: Mixed feelings about the newsgroup

As much as I rip on Usenet at times and especially sci.math, reality is I've spent a lot of time typing up posts like this one, and have to credit posting here with the worldwide rise of mymath, as in, the mathematics on my math blog, where I get visitors from all over the world. I first saw a world interest doing searches on my ideas and Usenet threads would pop up, which surprised me years ago. Today I take it for granted. And SOME postings like on my prime residue axiom simply take over huge swaths of search results—all to Usenet groups around the world as sci.math has country variants all over the world.

But I guess the reality is that Usenet is a way to communicate, and it's not about getting angry at the forum, or even the format which allows a free-for-all, nor does it appear to be useful to get angry with the hostiles who will work like mad demons to make your life miserable, like the ones who stalk my posts.

And they DO work like mad demons. In years past I'd be amazed at postings that would go 24 hours a day, with posters clearly working overtime trying to figure out what nasty thing to say to me that they expected might hurt my feelings or, their real goal, stop me from posting.

And readers may not realize that these people were confident of their ability to drive posters off of Usenet from EXPERIENCE. Some person would start posting about their math ideas and they would RIP on them, night and day—and that person would be gone.

I've watched them celebrate after in posts.

Free speech can be abused.

But as the years have gone by and I've learned to mostly ignore the worst of them, I've actually found use for negative feedback about my mathematical ideas, which is an odd thing because of its value to me—if someone shoots down an idea that's just it, it's gone. I forget the idea and can forget that person.

The fear I had in years past was that someone might put forward a BETTER IDEA, which was the scary thing which is why what I've done may not be safe for all discoverers who do not wish to be upstaged!!!

Oddly enough, the viciousness of the hostility may have protected me somewhat as posters were too afraid to say ANYTHING positive about my ideas knowing they'd be verbally assaulted if they did. The angry and nasty posters had made group rules that nothing good was to be said about my research, which is a set of rules they enforce to this day—posters know ahead of time they will be punished if they break them.

Hostile posters through the years have made it clear that you will be punished if you break those rules!

Just recently I got an email from someone expressing interest in my ideas but afraid to post.

So you could say the venom was like a protective screen. It annoyed me but did not stop me, but it stopped others cold.

The value of the negative feedback was shown yet again with my k^m = q mod N result, where I just didn't think about discrete logs at first as I'd never really thought about them before, and had this focus on solving for k. An argument with a poster got me to wondering, hmmm…can I find m, with k, q and N known using these equations? The answer was: yes.

Maybe eventually I'd have realized that but in a different situation it's quite possible someone else might have noticed before me, so another benefit to me of the vitriol and the rules against people posting anything positive about me or my research may be that I get to have all the major results!

History may reflect this saga as one of the most bizarre in human history, where a spate of mathematical discoveries in newly opened up areas were mine not because I hid anything, and not because there weren't smart people possibly able to figure things out before me—often I take months to work through various results—but simply because GROUP RULES on Usenet put the fear of the wrath of angry posters into the minds of people who might try. Or they simply never thought to try trusting the angry idiots.

At this date there's a well-worked system: I can post here without fear of positive responses. I take the negatives to help me kill bad ideas, and put forward draft posts. The best drafts I refine and put on my math blog or on mymathgroup or both. The most stunning results I send to the Annals of Mathematics.

That's the system. It is well established at this point. And I think it works well.

## JSH: Scary sense of responsibility

I use Usenet to talk out ideas, which I repeat a lot as there are all these posters who I used to call attention parasites who stalk my postings—for attention—who accuse me of posting JUST for attention, when I work out problems through posting. And the benefit of that was shown again recently when I focused on k, with my k^m = q mod N, or more succinctly, my mth residues result, and someone brought up discrete logs. And I pondered that for a bit and realized I could find m, when k, q a d N are known in a way that is actually one of my more "clever" results. It feels weird to so designate it myself but as a kid I'd look at certain solutions wondering if I'd been in the position of the discoverer, could I have figured that thing out? I think more so with the discrete log result possibly than others there could be people—like me as a kid—wondering, how did he figure THAT
out?

But here I'm not pushing my mth residue result yet again, having argued out a LOT of the issues with it, but now I'm considering an odd issue of social responsibility, where yes, I know there will be replies of outrage from the attention parasites who I also have called the angry idiots, but when I look at Google Analytics showing me hits from countries all over the globe to my math blog, it's not the same as someone else reading me claim to see that, who does not have his or her ideas out there, pulling that kind of attention.

That is an unimaginable amount of attention. And before the Internet not so easy. Getting ongoing interest from 40+ countries EVERY 30 DAYS for your ideas is not something that seems small to me, nor easily dismissed from my perspective.

I can quite simply project ideas worldwide. And if God help me I am this major discoverer then the social responsibility is what will define much of my life if that becomes widely known. I see replies that seem to think that fame on a discoverer level is about partying, or social prestige, or I guess all kinds of really fun things, when to me, it's about being forced into the position of being something of an icon, when I'm an iconoclast.

Maybe that's the weird contradiction that can destroy you—you fight, fight, fight against established ideas, and challenge other people to think versus just following along, or trusting "experts", only if you're really successful to one day BE the established ideas, and to be the expert. That sort of thing could really hurt a guy.

It's FUN ripping on the establishment. I actually play nice a lot of the time, but I am one of the few people on the planet who can actually go toe-to-toe with top mathematicians at any university in the world, and crush them without effort. Years ago when I was spending more time contacting math departments I was still surprised that I'd usually end up with the head of the math department in some kind of discussion or other, even if it was for him—it was always a him—to politely defer on something or other.

But it's been the same with math journals. With me, it just about always ends up with the chief editor getting involved. There at least there was once a she, but she begged me to quit sending her journal my papers! (I complied.)

No the bigger problem with going from being this angry person hollering on Usenet, and angrily decrying a math establishment that lost its way to being an accepted figure is losing that sense of direction, and having a responsibility to the world, to try and, gasp, be better? And no more hollering! No more letting fly with insults. No more abrupt criticisms.

Already I can push ideas through my various web presences, and it's so weird to contemplate it, and mostly just not do it. My words echo across the Internet, and I drive attention in all kinds of areas, and increasingly I realize that it takes careful thought and consideration when in that position. That there is a steep learning curve. That it's so much more scary than you would think just imagining it in the abstract versus living it.

Sometimes there will be posts where I give out instructions for world leaders or talk about advice to nations because I have a belief that you cannot learn to do something well that you've never practiced doing. IN my opinion God help the world if I sit humbly deciding that I can't be so arrogant as to do tests of giving such messages if later I'm considered the "expert" and such messages are required of me by my society.

If not? So what? Just one more angry idiot mouthing off on Usenet—a fringe zone where people can SAY anything.

In the last week, my ideas have been shown interest from people in over 30 countries.

Sure some Usenet poster whose ideas can't get much interest in his own country can dismiss that, or claim it's all robot programs, but that's because he doesn't have that attention for his ideas. There can't be that feeling of the bizarre when you just read about what some other person is facing.

My postings on Usenet don't impact things much, which is one thing that lets me continue to justify posting here, but even that's strange. Across a wide variety of areas I can see interest for my ideas from a world.

It occurs to me that I need to grow more, learn more, try more, practice a lot more, if I'm to ever live up to the potential responsibility which can some day be rested upon me. So this post is yet again, practice.

## JSH: Situation just became serious

My concern has been that fundamental equations in modular arithmetic could be exploited rather quickly and it appears with my latest efforts that that concern may be correct.

With the approach to discrete logarithms I've found it appears you CAN optimize the approach, and even though that involves looking for factors q^2 mod N, near N^2, it appears that it's easy to come up with a method that would allow factoring numbers on that scale as it's NOT a factorization where you don't have more tools from the idea itself.

Some of you may think this situation is a game. I assure you it is not.

My own hope had been that the research was far away from a trivial optimization but it appears that it is closer than I realized.

I would assume that there are people who are aware of that now as well.

It's not clear to me what to do, but my own hope is that some clear heads will realize the need to notify the US Government.

Unfortunately there may be enough in postings for a clever person to work out the details, which was not my wish, but things worked out faster than I realized until after postings. I often get my best ideas after posting.

Some sensible person needs to maybe quietly do their own tests and notify the US Government. There is no need to post about it on Usenet. I will not post further if I can help it after this post, and will not explain further, but may post again as I see necessary to try and help someone understand the seriousness of the situation.

Worst case can be a collapse of military grade encryption worldwide.

NO ONE is to use said information for stock trading. Or for any financial gain. The money will just be taken back from you later anyway.

Nations who get this message should simply go to procedures put in place for such an eventuality. World will probably be on various stages of high alert, indefinitely.