You misinterpreted me in your post #12. I said that semiprimes with factors greater than 3 were 1 or 5 mod 6, not that semiprimes greater than 3 were 1 or 5 mod 6.

Your claim that had “NOT been known for even a moment before [your] own research” has been known for hundreds if not thousands of years, and is taught in every undergraduate number theory class. Even basic textbooks like Underwood Dudley’s cover this.

You said that you doubted Silverman’s comment, so I’ll quote and source it here. He asked of your paper, “What kind of fruitcake spends the time to write 63 pages of Illucid word salad????? “. This can be seen at
http://www.mersenneforum.org/showthread.php?t=11539#post164086

Per your post on 4-15-09, here’s some info on e=mc^2:

http://salaswildthoughts.blogspot.com/2008/11/proof-for-einsteins-massenergy-emc2.html

http://news.softpedia.com/news/Einstein-039-s-Relativity-Theory-Proven-98461.shtml

As far as Clay Mathematics goes, they have two requirements: 1) the proof must be published in a recognized peer-reviewed journal and 2) must be recognized by the mathematics community within two years of its publication.

So obviously, it is absolutely important to get the paper out to mathematicians for pre-print first. If the paper were published in a journal with an error, then it would cut into that 2-yr time limit imposed by Clay.

Before I sumbit this proof, I would like to publish a few elemetary proofs separately from the paper so that they can be reviewed and established for me to reference. This way I could take them out of this paper and just reference them. I’m giving it a lot of thought these days.

But you’re right, the prize from Clay certainly would help in many ways.

Jeff

While I understand what your comment means, I feel I ought to explain it to others who may not understand.

“That all primes (and semiprimes with factors) greater than 3 are either 1 or 5 mod 6 has been known for hundreds of years.”

Semiprimes all have factors first off, and not all of them greater than 3 are 1 or 5 for the modulus 6. Take 4 or 9, neither these, the first two semiprimes greater than 3, are 1 or 5 mod 6. See, 4 % 6 = 4 and 9 % 6 = 3. So, no, this has not been known for hundreds of years. What I think you mean is that it has been known for hundreds of years that all primes > 3 and products of primes (>3 exclusively) are 1 or 5 for the modulus 6. But I’m not entirely sure how that relates with anything I said.

However, what has NOT been known for even a moment before my own research is that all primes > 3 and products of primes (> 3 exclusively) have the following characteristics:

Alpha Q’s, products of primes (> 3 exclusively) that = 5 with a modulus 6 are a product of an Alpha Number and a Beta Number.

Beta Q’s, products of primes (> 3 exclusively) that = 1 with a modulus 6 are a product of either 1) two Alpha Numbers or 2) two Beta Numbers.

Alpha Number, primes > 3 or a product of primes (> 3 exclusively) that = 5 with a modulus 6.

Beta Number, primes > 3 or a product of primes (> 3 exclusively) that = 1 with a modulus 6.

This is highly significant. And even if someone somewhere has found this also in the past (I know of no where it is published or even touched on), it matters little. It’s still a fact and very telling when it comes to Prime Correspondents. Mathematicians can appreciate this immediately upon seeing it.

So, yeah, this is just laid out for others, as I think many people will read your first paragraph and be confused with what you are trying to state.

As far as Silverman stating my paper is “word salad”, I doubt it. He’s highly intelligent and experienced in factorization and not someone who would overlook it so easily and brush it off as this. Don’t know where you got that. If it is true, then I think one of two things 1) he’s losing his touch with age or 2) he was premised that it was “word salad” before he even read the first page and therefore didn’t get passed the first page. Probably presented to him while he was trying to watch tv or something. Mathematicians are very busy generally and often have their minds on other things (often pertaining to their own research) and occasionally don’t care to be distracted with new things. This paper is really for the next generation of mathematician or those still willing to learn. But then again, there has been some cynical / condescending things that have fallen from his lips over the years, so it probably wouldn’t surprise me completely. I just doubt it.

Now, as far as “if there’s anything there I can’t find it,” I just can say that I don’t know your skillset and it doesn’t appear you are a mathematician by your posts (for instance, your first paragraph). So, I’m not sure how you would be able to find it. It’s really not for the lay person or even the undergrad student. But I would be happy to help you through it if you’d like.

“I take it from your response that you wouldn’t be willing to do any kind of demonstration.”

I don’t know how you got that out of it. Right now I have been presenting my work to potential investors. Soon, as our funding goals are reached, demonstrations will be had for the public.

“investors as well as academics would know you were onto something.”

Many already know what we’re onto, but we do appreciate it catching on even more. My personal first step was doing the math. Then writing the paper as best I could to share what I learned with others. Then make inventions based on these findings in order to build on the math. Then patent. Then sell. Then when I am old and retired, then I will concern myself with the rest of the world. In the meantime, we have much work to do.

Jeff

That’s rather generous, I’d say. There are lots of very difficult things that have been known for hundreds of years (solving the general cubic equation is pretty tricky and it was done at least 450 years ago). Showing that all primes greater than 3 are either 1 or 5 mod 6 should take a moderately intelligent 12 year old less than half an hour.

I take it from your response that you wouldn’t be willing to do any kind of demonstration. But how, then, to convince ourselves that you have something? Dr. Silverman of MITRE Corp. has characterized your proof as “word salad”, and I’m inclined to agree — if there’s anything there I can’t find it.

But if you would just demonstrate something thought to be difficult — factoring a hard number, solving large 3-SAT instances, etc. — investors as well as academics would know you were onto something.

Could you please cite a reference for your statement above, “In fact, it was just this past year that Einstein’s e=mc^2 was mathematically ‘proven.’”

Also, you might go a long way to bolstering your claims by:
1) publishing this in mainstream mathematical journals.
2) actually cracking some RSA encryption.
3) claiming the $1 million prize from the Clay Mathematics Institute for your proof of the Riemann hypothesis (hey, that’s funding plus a media appearance plus recognition by the broader mathematics community).

“To simplify, all primes are either 1 (Beta) or 5 (Alpha) when p mod 6. All Beta Primes are a combination either two Betas or two Alphas. All Alpha Primes are a combination of one Alpha and one Beta.”

Should read “All Beta Q’s are…” and “All Alpha Q’s are…”

And I forgot to mention that all RSA’s public Keys are Q’s, either Alpha or Beta.

Thanks,

Jeff

Your tone sounds surprisingly similar to Mr. Fred P. on Schneier’s blog, but maybe it’s just me.

“I’m glad to see you no longer claim to be able to crack RSA. Nice editing job.”

Never did claim such and you surely know that. And I do not do the editting here. I make notes on sentences in the site that must go and send them off.

“May I ask what natural principles govern the distribution of the primes? Or is this too a trade secret?”

No trade secret…it’s in my paper. Primes are distributed in the absolute shortest distance from one another analogous to cycles per time. If you take a chromatic musical scale and begin counting the primes, they all fall into a hexagonal mode (hex being 6 notes of course) and they never fall out of that mode.

The natural principle: frequency
Integers: a grouping of infinite fractions into a single value
Neutronics: combining the two with clock mathematics

To simplify, all primes are either 1 (Beta) or 5 (Alpha) when p mod 6. All Beta Primes are a combination either two Betas or two Alphas. All Alpha Primes are a combination of one Alpha and one Beta. All numbers n mod 6 = 1 or 5 are either prime or multiples of Alphas or Betas, which includes powers of Alphas or Betas. I have grouped them with what I call simply Correspondents Y and X, which can be any arbitrary Integer.

While RSA uses Integers only, our algorithm uses the fact that one cannot calculate m with any certainty by only knowing d & n in the Neutronic Equation below:

n = (m – m % d) / d

However, you can calculate n by knowing m and d. In primes, and thus RSA, d = 6 in terms of its Correspondents. In NEA, d is arbitrary and can even be a decimal, while n will always be an Integer, thus burying both m and d into the abyss of infinity.

Hope that explains it better.

Thanks,

Jeff

In response to your first comment:

I can certainly appreciate skepticism. “Doubt” I’m not sure about though. On what grounds would you have reason to doubt when you do not know our work? The only people who have seen the patent as of yet is the U.S. patent office.

Now, skepticism I can discuss. I can understand skepticism, as many have tried to find fast methods for factoring large numbers throughout history. Bill Gates stated years ago that this would represent the greatest breakthrough in mathematics in terms of computing…not that he’s an expert in mathematics–it’s just that it’s widely accepted. The question then does come about, why would I have succeeded when all others have failed? Thus, the skepticism arises. Problem is, the question itself is flawed, ’cause I never stated that I have succeeded at this. Could I factor the example you gave me? I believe so. But will I demonstrate it now? No. The reason why will become clear in the coming year if matters fall into their proper order.

I can tell you just by briefly looking at this number, however, that it is a Beta Number (Qb), which is either a product of 1) two Alpha Numbers or 2) two Beta Numbers and not one Alpha and one Beta (Alpha Numbers mod 6 = 5 and Beta Numbers mod 6 = 1). This is in my paper. And secondly, no one working with RSA’s factors consider this a “small” number. I understand that “large” and “small” are relative terms. But I would view any value that takes the best available sieve to factor it in less than a minute is a small number. A number that can almost be reached by a less than perfect sieve is still quite an extraordinarily large number.

The extent of my public claims rise and fall on the points in my blog above. Anything found on this site prior to the blog is not necessarily my claim. I do not write the content for this website and on the patent itself I did not claim such. In fact, I do not believe I saw on this site ever where it was stated that we could factor such large numbers quickly. It was written that they could be factored quickly by being able to calculate the first couple of digits, and I asked that this wording to be removed and it has been. While I personally believe that to be true, RSA does not. And yes, it is in my patent that I have found a way to calculate the first couple of digits of RSA’s public keys.

In response to your second comment:

Where I said, “large numbers identical to those produced from RSA’s algorithm”…

It is quite a jump from this wording to your…

“Would you post a factor for RSA-768? (RSA-2048 would be nice as well.)”

I say, it would NOT go a long way to convince people “that [I'm] not just making this stuff up”. If I alone admitted that I could do this and then did it, I would have many more problems than I already do. Hackers have been all over my computer these past few weeks from all over the world looking for such information. One or more have even been using my Internet computer as a test bed (against my will of course) for the latest version of the Conficker virus long before it was released publicy yesterday. So yeah, if one were able to do such a thing so quickly, it would be foolish to reveal this without first taking proper precautions.

So please do not raise this again to me. On the record, no, I cannot perform such challenges for you.

Thanks,

Jeff

Whenever you see a limit in my paper beginning with 1, that of course means when x (from the function) = 1. In this case, b (x) = 0, where x = 1.

I apologize to readers for this confusion. When I move on to fix the typos and other errors in the paper, I will include this as one. But really, did you not know what was meant by that?

Jeff