Hello my old community. I'm going to be publishing my proof soon,  but I've solved the conjecture about 7-8 years ago.   Ive been sitting on the solution for a long while.  Since the introduction of LLM's ive taken the opportunity to test the consistency of my answer.     Following the solution, ive found a couple interesting patterns in primes reciently as well.   It seems to have a connection to the reinmann hypothesis. Namely the 1/2 part.  - The density of primes is contained in the first half of all numbers.   For m, m composite ..read more

How do write a combination of y and x on a graph calculator? If you want to calculate y not x ..read more

This  is about the paper "Fast contact force computation for non-penetrating rigid bodies".  Has anybody made sense of this?  I have questions.  Do I completely neglect the unprocessed a's that are neither mc nor c?  If the sign for an unprocessed "a" changes, should I stop and pivot and put that index in either nc or c?  I know that the unprocessed "f's" remain zero, but what if the sign of an unprocessed  "a" changes?    Do I actually perform a pivot operation on a matrix? Or is that done by moving between a "c" and an "mc ..read more

Scale over 20 years ago. I program now the fractal carbon colors. Each pixel contains 256 * 256 mosaic information, resulting in an image resolution of 216 (65 536 ..read more

My new issue in my journey to try to understand infinity concerns the "ends" of infinity. I was told on here that the infinite sum of 1/2^n = 1, and not just gets close but actually equals 1.   I can't help but notice that we are giving infinity a definite beginning point at 1/2 and a definite end point at 1.  What could n possible equal to get to this point? If this last point really is a solution to the equation, then wouldn't it have to be 1/infinity, or in  other words, the "infinity-ith" point?  If so, how can it be said that the natural numbers can numerate all p ..read more

The two sets N (naturals) and I (integers) have a one-to-one correspondence and are said to have equal size/cardinality.   But if we put them one-to-one in a specific way, such as the naturals to the naturals from I, we see that the naturals of I get used up leaving 0 and the negative integers. This seems to show that a correspondence from N to I can also not be one-to-one.   The curiosity I get from this is just too much.  It almost seems like this is an example of something that can be proved to be true and can be proved to be false.  I would ..read more

What is functions simplified and detailed ..read more

We consider a linear vector space V of dimension n. W is a proper subspace of V.We take a vector 'e' belonging to V-W and N vectors y_i belonging to W;i=1,2,3…N;N>>n the dimension of V. All y_i cannot obviously be independent the number N being greater than the dimension of V the parent vector space; k of the  y_i vectors are considered to be linearly independent where k is the dimension of W. The rest of the y_i are linear combinations of these k, basic y_i vectors of W. We consider sums   αi=e+yi;i=1,2…N (1) Now each alpha_i=e+y_i belongs to V-W. We prove it as follows If pos ..read more

I have been stuck on this problem for awhile and have no sense of it, I have gotten stuff written down but sadly don't have any confidence in my answer. Any help would be absolutely appreciated thank you!! This is what I have now. $$ \begin{array}{l} \mathrm{W}^{\perp}=\{p \in P 2 |\langle p, x+1\rangle=0\} \\ \langle p x+1\rangle=p(-1) x+1(-1)+p(0) x+1(0)+p(1) x+1(1)=p(-1) \\ (-1+1)+p(0)(0+1)+p(1)(1+1)=p(0)+2 p(1)=2 \mathrm{p}(1) \end{array} $$ since we are looking for polynomials such that $\mathrm{p}(0)=2 \mathrm{p}(1),$ and with the definition of $\mathrm{P}^1$ all polynomials $a x^2 ..read more

I had this idea and I think it belongs to Algebraic Topology but here it is: Imagine some object C in some non-Euclidean space K such that object C is constantly being transformed in some important way every time this object moves in K but only because it moves through K. If it moved through some space M, then it would transform but differently or not at all. Is there a theory about objects like these and spaces that manipulate objects ..read more