A prime counting function I have never seen

[fresh_42]

Oh I am well aware of the Riemann hypothesis. It drives me nuts as I can’t deal with anything too abstract. Hence my problem with advanced mathematics. It doesn’t stop me from trying though.

Fermat claimed to have proven something and it took 350 years and a lot of very difficult mathematics to prove it. I don't say "again" since nobody truly believes Fermat had a proof. However, his claim led to the development of entire branches of mathematics.

Just make sure you won't try what already has been proven impossible:
A cube cannot be doubled by using a straightedge and compass.
A circle cannot be squared by using a straightedge and compass.
And an (arbitrary) angle cannot be split into three equal parts by using a straightedge and compass.

Here is a nice anecdote about the Riemann hypothesis:

It is not quite clear whether Hardy believed in God or was just superstitious. However, in any case, he believed God would do everything to make his life tough and complicated. One day he was on a journey back home to England. (I've heard it with Harald Bohr and Copenhagen, but also found Norway on the internet.) Anyway. He had to take a ship and the boat he got didn't look very trustworthy. Typically, he thought, why me?
So he sent a postcard before boarding - say to Bohr - claiming he had found the proof of Riemann's hypothesis.
When afterward asked why, he replied: Well, if the ship sank the proof would have been lost but I would have become the most famous mathematician of my generation. God won't allow this to happen. This way I only had to write Bohr another postcard in which I stated to have made a mistake.

 

[logistic_guy]

Thanks for this.

You're welcome

First off it was my mistake to say work as this is my hobby. Not career.

That's very interesting.

I was pretty upset that the golden ratio didn’t work out. But it did lead to the basis of this latest formula.

I call this golden ratio Magic. Last year in October a member threw a problem in this forum and we magically and precisely solved it by the golden ratio. Since you're interested in this golden ratio, you may want to take a look at here:

Brain teaser

Hi, I stumbled upon this question on Facebook and I tried to solve it unsuccessfully. I saw in the comments people talking about symmetry in their solutions but I didn't understand them. To me it seems there is insufficient info because the heights and widths of A and B share constraints, but...

www.freemathhelp.com

As you can probably tell from my vids I just play around and sometimes stumble across something interesting. Unfortunately it usually takes me awhile to figure out how I found it if I find it at all. But this formula does seem to be special. I’m just throwing it out there and hoping someone can do something with it.

If you want to progress further with your discovery and to be able to prove claims, I advise you to study number theory and abstract algebra (there are a lot about prime numbers there). This abstract algebra will sound confusing at the beginning, but once you proceed further, you'll find it fun to learn. Even if you find the first few chapters are easy to learn, don't skip a single page because the basics what make things become beautiful later.

I don't like to compliment people, but I will be honest with you, fresh_42 is a Genius professor. He has a great knowledge in mathematics, especially number theory and abstract algebra. If you decided to study them and had questions, I am sure that he would be so glad to answer your queries in a fantastic way. I myself have learnt a lot from him and still learning.

Also read and study every post and link he has given you carefully. Sometimes, you will need to spend a week or more reading to understand a specific idea from the book. The same idea can be understood in 15 minutes or less in a simple post written and explained by professor fresh_42.

There are also other great instructors on this forum whom I am sure will be glad to help you, but I’ve made professor fresh_42 my first priority. He is just a super Genius naturally.

Why the careless whisper reference? Did I have it playing in the background ground of one of my vids? lol

I think you created a playlist in your account and then forgot about it

Careless whisper is one of the first videos in that list.

 

[binbots]

Fermat claimed to have proven something and it took 350 years and a lot of very difficult mathematics to prove it. I don't say "again" since nobody truly believes Fermat had a proof. However, his claim led to the development of entire branches of mathematics.

Just make sure you won't try what already has been proven impossible:
A cube cannot be doubled by using a straightedge and compass.
A circle cannot be squared by using a straightedge and compass.
And an (arbitrary) angle cannot be split into three equal parts by using a straightedge and compass.

Here is a nice anecdote about the Riemann hypothesis:

It is not quite clear whether Hardy believed in God or was just superstitious. However, in any case, he believed God would do everything to make his life tough and complicated. One day he was on a journey back home to England. (I've heard it with Harald Bohr and Copenhagen, but also found Norway on the internet.) Anyway. He had to take a ship and the boat he got didn't look very trustworthy. Typically, he thought, why me?
So he sent a postcard before boarding - say to Bohr - claiming he had found the proof of Riemann's hypothesis.
When afterward asked why, he replied: Well, if the ship sank the proof would have been lost but I would have become the most famous mathematician of my generation. God won't allow this to happen. This way I only had to write Bohr another postcard in which I stated to have made a mistake.

lol. Sooo what you’re saying is I should have shown my equation with the caption: I solved the prime number theorem. Unfortunately I don’t have the time to write it all out.
Then I should have just disappeared. Ok next time I think of something that’s how I will play it. lol.

As for the Riemann hypothesis give me a day or two to respond. I have my own ideas on how that works. My ideas may not be correct but they are unique.

 

[binbots]

I forgot to mention that some theorems about the prime number density require the Riemann hypothesis to hold and I'm not certain whether Rosser's result does or does not. You can find a short description and some links about the relationship between [imath] \pi(x) [/imath] and the Riemann hypothesis here:

The History and Importance of the Riemann Hypothesis

The history of the Riemann hypothesis may be considered to start with the first mention of prime numbers in the Rhind Mathematical Papyrus around 1550 BC.

www.physicsforums.com

I made a video explaining why I believe this works. Hopefully you have 11 mins to spare.