prime numbers distribution

This isn’t a property of prime numbers. It’s an artifact of the visualization. On a spiral, any regular selection—multiples of 3, arithmetic progressions, 6k +\- 1 will line up into clean rays or curves just as nicely. The pattern comes from the representation, not from primes.

The explanation is just as cool as the gif:

i want more of this on my feed!!

Surely this isn’t true… if there was a pattern, they wouldn’t be so hard to find.

This is not some special attribute of primes! The distribution of all numbers give you a complete spiral!

I’m not a mathematician, but I’m gonna call bs. I think someone decided they wanted to make a spiral pattern, and then worked backwards to find a way to make a representation of prime numbers fit a spiral.

The spirals have nothing to do with prime numbers. This is how whole number distribute on that coordinate system.

Pointless. Just a visualisation.

but fun

It was perfect even before it completed

would you look at that

3D version:

This very same pattern occurs for all numbers, not just prime numbers.

#Chronoflux Temporal Hydrodynamics.

@grok is this animation accurate?

Fibonacci

@grok what does a dot here exactly represent? I mean I know it's supposed to be a prime number but how is it related to its x and y coordinates in that video?

no, wait, what?

This pattern is not unique to prime numbers and not happening because they are prime numbers.

Greek philosopher and mathematician Eratosthenes invented the algorithm for enumerating all the primes knows as "the sieve of Eratosthenes, which lends itself to a 2D layout on a square grid because one only has to use a number's factors up to the square root of that number. He was also an astronomer who created a book cataloguing known stars in a rough order of brightness that included 675 stars. There are exactly 675 primes up to 7 factorial, aka "Plato's number" (the number of citizens in the city in Plato's Laws). 5040 plus 1 is a perfect square (71^2), and 5040 minus 1 is prime. Incidentally, 71 is the 20th prime number and primes that high were certainly know to Plato. He remarks in the book that the process of recording fainter and fainter stars is straightforward but endless, and gets slightly harder as you go along. He doesn't say, but we can deduce, that he used his own algorithm starting with a square 71 on a side. Striking out each box in the pattern using the 20 prime lengths recorded on the first, length 71 side suffices to leave behind the pattern of primes up to 5040. I'm saying Eratosthenes was probably the first human being to see this visual pattern. He lived from 276 to 194 BC.

Looks like a spiral galaxy.

what does the angle represent?

Need my Prime sorting engine? 0 sieves involved, pure sort engine based of rules that catches every prime in any interval no matter how large, beware computing power is needed or it may melt your device. As a flex also sorts all Marsennes for you 😁😁 hope it helps!

i think about the 2 opposing gaping gaps every day

If prime numbers follow this spiral in this mode of representation, can we use it by extrapolating the arms of the spirals, in order to obtain privileged zones for searching for ever-larger prime numbers?

I bet this bad boy pisses off so many math nerds

Beautiful.. Prime spiral + Riemann zeros Φ(p) = Re[Σ exp(iγ log p) / √(¼+γ²)] Primes glow where the zeros constructively interfere. 97% detection accuracy at n < 100. Code:

Wtf are the axes here?

@SunWeatherMan Spiral out.

It makes people believe that there is some magic. But, the way this is plotting is not explained and this is the key - any sequence of numbers will result in spirals, i.e., archimedean spirals

well well well, golden ratio once again

What does this even mean? What is the x-axis? What is the y-axis? Also: not true. Prime numbers are hard to find. If they had such an obvious pattern, we would have a deterministic algorithmic way of finding them now.

Please watch this fantastic video which helps to explain this pattern.