116 reputation
4
bio website
location Colorado
age 27
visits member for 1 year, 9 months
seen Sep 4 at 11:16

I'm a coder


Sep
24
awarded  Autobiographer
Mar
28
comment A question on pure math research for integer factorization
To clarify the triple component, in my construction, p^r + q^r = a^r yield triple (p,q,a). I assert you cannot form a Pythagorean triple out of at least one of these sets. thus r = 1 and from our prior knowledge p + q^r = 2n implying a = 2n
Mar
27
comment A question on pure math research for integer factorization
I'm trying to use Wiles work on fermat's last theorem to force my power of primes exponent to 2 or 1. The key is further forcing the exponent to 1 by eliminating the 2 case for some pair. I think this part is trivial compared to application of Fermat's last theorem, which requires very powerful machinery involving elliptic curves.
Mar
27
comment A question on pure math research for integer factorization
p and q are also prime I should mention
Mar
27
comment A question on pure math research for integer factorization
Yes I have and I'm not going to discuss what I mean by pair outside saying that a pair is a set of two numbers (p,q^r) such that p + q^r = 2n for any integer >= 8. Raise p to the r power and you can generate p^r + q^r = a^r and show that there exists a pair where a is an integer. Therefore, r <= 2. Show that one of these pairs cannot be a pythagorean triple. Therefore r is equal to 1
Mar
26
comment A question on pure math research for integer factorization
"any even number can be expressed as the sum of a prime and a finite product of primes" Let me refine what I meant to say. I proved any even number can be expressed as the sum of a prime p and the product of the same prime q (2n = p + q^r) where q is prime. This is not a restatement of the fundamental theorem of arithmetic
Mar
26
awarded  Commentator
Mar
26
comment A question on pure math research for integer factorization
You're rght that I've reproved results from hardy and chen but using a bounding argument that lets me generate specific sets of solutions. I'm thinking I can use fermats last theorem to reduce r to 2. But here is the cool part, there appears to be a way of showing one of the pairs can't be a pythagorean triple. Thus r=1
Mar
25
comment A question on pure math research for integer factorization
And I'm sorry Will for being snippy, but as an MSRI mathematician you know that some things can be said about factorization outside of an O() algorithm. For example, any researcher studying the collatz conjecture eventually stumbles upon the realization that if one reaches a 2^n factorization from an arbitrary one in a finite sequence of steps, then the problem is resolved. In essence it is a problem about movement around particular factorizations.
Mar
25
comment A question on pure math research for integer factorization
As I have reduced the problem to finite sets of a certain structure, I already know a great deal about the particular factorizations. I just need to know how they could change under addition within my finite range. I've constructed some rings to study the structure, but nothing obvious has occurred to me yet
Mar
25
comment A question on pure math research for integer factorization
I found a pattern while studying the goldbach conjecture that relies upon a certain feature of certain factorizations. It's very easy to test and has held for an enormous set of numbers thus I believe it is interesting to study. After exploring it for a bit, I was able to build a bound based on the product sequence of gaps between the greatest and lowest prime in a related factorization of 2n - (certain primes) thus showing any even number can be expressed as the sum of a prime and a finite product of primes. I want to reduce the finite product to one obviously, but I need more info on IF.
Mar
25
comment A question on pure math research for integer factorization
Furthermore, prime numbers do not exhibit a random distribution therefore it stands to reason that factorization patterns are also not random. I understand the difficulty in saying interesting things about them, yet one really could if he wanted. If you don't know, then just say so. Please don't just shoot me down and offer no help.
Mar
25
comment A question on pure math research for integer factorization
first, please lay off the condescending attitude. There has been over 2000 years of research studying IF. Yes you can say some things. Second, I have significant numerical evidence to suggest what I'm trying to prove is true (up to 4 X 10^18). Third, most research papers study efficient algorithms thus making it difficult to find papers focusing on certain patterns outside the work of Hardy and Tao.
Mar
24
comment A question on pure math research for integer factorization
That's the point. There has to be some body of research attempting to say something
Mar
24
awarded  Student
Mar
24
awarded  Editor
Mar
24
revised A question on pure math research for integer factorization
added 612 characters in body
Mar
23
comment A question on pure math research for integer factorization
I'm sorry I think I deleted your comment. I feel terrible about it
Mar
23
asked A question on pure math research for integer factorization