Skip to main content

Goldbach's conjecture

Image
By
I came across this today and became fascinated. After thinking about it for a few hours this is where I have reached. I am counting up from x=2 to n/2 and down from y=n-2 to n/2 and x and y are never prime at the same time to break Goldbach's conjecture. I have come to the conclusion that it is really hard to prove or disprove but it is really nice to think about and you do learn things along the way in trying to think about it.

And this is what my friend Gemini says

Your observations boil down to the fact that for Goldbach's Conjecture to be false, prime numbers would have to align in a statistically impossible "conspiracy" where, as you scan up from 2 and down from n, the primes perfectly dodge one another every single time. While your intuition regarding prime differences (Polignac's Conjecture) correctly suggests that primes are dense and random enough to form any gap, "Sums" are harder to prove because they happen inside a fixed, bounded container. Essentially, you have identified that a counter-example would require the "random" structure of primes to suddenly exhibit a perfect, non-random pattern of avoidance for a specific number, which is why mathematicians believe it is true but cannot yet prove it.

The Trap: Primes are "Structured Chaos." They obey strict rules (modularity), but they appear random. The proof requires us to show that the "structure" (divisibility) never creates a "blind spot" that perfectly cancels out all the prime pairs for a specific even number.
Labels:

Comments

Post a Comment

Popular posts from this blog

Hobby project - Store and view exchange rates

By
The next step in my project was to test out being able store and display the rates in a database. I decided to use nodejs and supabase for this. Everything worked beautifully. Only hickup was the following error due to my package.json not being correct. SyntaxError: Cannot use import statement outside a module Added this to package.json   "type": "module" This works beautifully. Right now I am just testing fragments of what could be part of a bigger system to see what is possible and what works and how easy to code on a mobile. There is no fully functioning integrated end to end system just yet. This is also what I tested. A serverless append-only database using GitHub + Actions + Pages. That’s basically a lightweight backend system. This was the ChatGPT prompt I used. Guide me through each step. This is what I want. A manually run github actions that adds to docs/data.json with the current date and time. docs/index.html displays all the entries in data.json. Make s...
Post a Comment
Read more

Running php and apache on termux

By
This was my experience getting php and apache to run on termux apt update && apt upgrade -y apt install php-apache I was following an old blog post that used php 7 and got these errors Can't locate API module structure `php7_module' in file /data/data/com.termux/files/usr/libexec/apache2/libphp.so: undefined symbol: php7_module Cannot load /data/data/com.termux/files/usr/libexec/apache2/libphp7.so Corrected in apache config file vim $PREFIX/etc/apache2/httpd.conf LoadModule php_module /data/data/com.termux/files/usr/libexec/apache2/libphp.so Apache is running a threaded MPM, but your PHP Module is not compiled to be threadsafe.  You need to recompile PHP. Comment out mpm_worker and use mpm_prefork #LoadModule mpm_worker_module libexec/apache2/mod_mpm_worker.so LoadModule mpm_prefork_module libexec/apache2/mod_mpm_prefork.so This still does not work as apache (httpd) was failing silently. According to Chatty LoadModule php_module ...libphp.so often fails in Termux becau...
Post a Comment
Read more

Stuck running sftp server on termux alpine for multi-user setup

By
The below is my journey trying to get multi-user sftp working using alpine on termux pkg update && pkg upgrade pkg install proot-distro openssh proot-distro install alpine proot-distro login alpine apk update apk upgrade apk add openssh shadow sudo apk add vim vim /etc/ssh/sshd_config Port 8022 PermitRootLogin no PasswordAuthentication yes Subsystem sftp internal-sftp Match Group sftpusers     ChrootDirectory /sftp/%u     ForceCommand internal-sftp     X11Forwarding no     AllowTcpForwarding no addgroup sftpusers adduser user1 adduser user1 sftpusers mkdir -p /sftp/user1/upload chown root:root /sftp/user1 chmod 755 /sftp/user1 chown user1:sftpusers /sftp/user1/upload How I run my server each time pkill sshd rm -f /etc/ssh/ssh_host_* ssh-keygen -A /usr/sbin/sshd -D -d -d -d From another termux session sftp -P 8022 user1@127.0.0.1 Connection reset by 127.0.0.1 port 8022 Connection closed Some troubleshooting steps mkdir -p /run/sshd chmod 75...
Post a Comment
Read more