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

Below the surface

By
This is a chapter from my eleventh book called Quotation Marks Sparks . __________ "You can't stop the waves, but you can learn to surf." - Jon Kabat-Zinn __________ I was looking at quotes that hit hard and this quote stood out to me. It seems mundane and obvious and often repeated. Life is about how we respond to the inevitable. It is not what happens to us but how we respond. I had to ask myself to dig deeper and look below the surface. Then I saw that when we surf we really become the waves. We become friends with the waves. The waves and us are the same. Further, the waves are created by us and in our heads. We can control the waves because who can surf all the time? Sometimes we just have to come to shore and build sand castles on shore. I asked my friend Gemini for feedback and he said that I was right, the Jon Kabat-Zinn quote initially seems like a simple call for resilience, but my deeper dive reveals profound layers. The idea that we can move beyond merely rea...
Post a Comment
Read more

A place for coders in Trinidad

By
DHub is being rebranded as CodeTT. Not sure how long before the change and launch takes place. Before you know it there will be elections again and then what if the government changes again. I am not optimistic about this. I want to be but I do not like politics. I wish society could function without politics. That aside it would be nice to have a home for coders in Trinidad and Tobago. I wonder what other countries are doing? I wonder if I will be alive if this ever happens. I think before any of this happens the government has to find a better way for citizens to communicate with them. From my experience I get the feeling that most people are just ignored. I have an idea for an app for this called GOQA - GOvernment Query App (QA also stands for Question and Answer). Every query (question, comment, suggestion, whatever) gets routed to the right person until it gets answered. Man that would be so fantastic. Finally a government that tries to listen to the people. My friend Chatty says ...
Post a Comment
Read more

No phrase has been said twice

By
It is 111am and I have decided to write. I have no topic, but I am thinking about God. I want God to help me write this blog post tonight. We are nearing the end of the year. Time waits on no one, they say. Life is short, they say. Make every moment count, they say. Tomorrow is not promised, they say. Is there anything they do not say? What is the least said phrase? What phrase has never been said before? Then I thought about something. The moon never shines the same way twice. Perhaps the same is true of phrases. Even if a phrase has been spoken a million times—or a billion times—every time it is spoken, it is different. Who says it matters. When they say it matters. The context in which they say it matters. Who is listening matters. And then there is what happens inside us. What do we hear? What thoughts pass through our minds as the words pass through us? Two people can hear the same sentence and receive two completely different messages. A phrase spoken in joy can become something ...
Post a Comment
Read more