Truncated Prime Pictures

Is it just the last digit that causes primes not to be normal numbers? As in is it the lack of ending in 2,4,6,8,0 that means the walk on them doesn't look random like pi does? This post looks at the same walks as the other recent posts but with the least significant dropped.

I made the graph dropping the last digit from each prime. The walk looks different but not that different. similar to some of the other walks I calculated

I made a barchart of the counts of digits in prime numbers up to 10138889.

The same graph not including the final digit also shows this truncated view is not normal either. A graph of the truncated counts on all numbers up to 10158737 is 60 million digits

This really does look normal. So it looks like Prime numbers except the least significant digit might be normal but making a walk with them still shows them moving from the origin at too quick a rate to be really a random walk in the digits.

I made a heatmap of which numbers follow each other in the primes up to ten million digits.

and the primes except the last digit

Code is here

More Prime Pictures

Smarandache Sequence as a horizontal color representation. First digit is the first pixel top left. Each number is its own color. Move one step to the right and each 1000 drop down a step. Code is here

Thsi idea is from Walking on real numbers though they did not look at the prime number concatenated.

Using the first 11066873 prime digits if the previous number was smaller go up a step if it was larger go down a step. The path crosses zero the 204 times.

Using the first 2010484 prime digits if the previous number was smaller go up a step if it was larger go down a step. The path crosses zero the 197 times.

I am still not sure these pictures mean anything.

Number Sequence Walks in One Image

To show each stage of the pattern these number sequences make I have changed my script here to zoom out each order of magnitude. This means the path up to 100,1000,10000,100000 and 1000000 will all show up as similar sized. Though coloured differently.

Prime Numbers

Champernowne Number is similar but there are some differences.

even Numbers

Odd Numbers

Nearly Primes (numbers that are not divisible by 2,3,5,7,11,13,17,19) are added tot he string to walk. This walk will be all primes and a few numbers that aren't. The graph is more similar to the prime graph (and I got the scaling a bit wrong at the start )but I am still surprised at how different it is.

Zooming in on the loop in Smarandache Sequence

What is going on in the loop here at the bottom right that causes the turtle to change direction? In the Ten thousand digits path it is some of the orange and light purple parts below

to draw just this loop part of the image the code is here. Zoomed in the path looks like this

This image contains the 279 primes from 14503 up to 17183

In the 100K image it seems to be the over 2000 primes between 152003 and 178361 that make up this loop part

Fractal Pattern in the prime numbers

The Smarandache–Wellin number is made by sticking together all the prime numbers.

2 add on 3 add on 5 add on 7... to make 2357111317192329

A reddit user improved my earlier code with generators. That old code is here. And using the generators from this code I got a prime number checker from here.

With 10k steps this looks like

100k steps

and a million steps (digits)

Five million digits

1000 digits from primes

100 digits looks like an album cover

Here every one tenth of the total distance changes the colour so roughly the blue part on the top left is the previous image. These are primes in the base 10 which is probably why the pattern repeats like that.

These seem really similar to each other. The Champernowne constant seems to do something similar, so maybe most sequences of natural numbers stuck together make repeating patterns like this. I tested the even and off numbers and they kind of do.

even numbers 100k digits

odd numbers 100k digits

The code is here so you can play with it, find bugs and recreate the images. Thanks to the help to the reddit user who recreated the images in Mathematica, code here as a sanity check.

Numbers from a sequence in the base ten make a similar pattern that gets ten time bigger each round. Which doesn't sound surprising said like that. Still the pictures look cool I think.

Champernowne constant might form a fractal

Making each digit of Champernowne constant a step in a logo turtle picture seems to form a fractal picture.

10k steps

100k steps

2 million steps

It seems to form this circle with another below and to the left over and over again.