Fraction of Primes 2

The fit for the fraction of numbers that are primes posted a week ago can be modified to approximate a known result by using ln(n) instead of log₁₀(n) and rearranging terms somewhat to get,


The empirical fit gives the power of ln(n) as slightly more negative than -1. For more information see the Wikipedia article on the prime counting function.

The Fraction of Primes

A prime number is a number which is not devisible by any numbers except for one and itself.

I just did a curve fit for the fraction of prime numbers less than or equal to a given number and found a reasonably good fit shown in the plot below. This is probably not a new result since I once saw something similar for a bound on the number of primes. It is just the empirical fit that I found. The fraction of primes is the solid line and the fit the dotted line.

The Octal System

This is a short poem that I wrote about 1982 in an effort to associate octal numbers with some basic concepts. It was inspired by the binary number system which associates 1 and 0 with "true and false", "yes and no" or "on and off" and also by aspects of "yin and yang." So here is,

The Octal System

 001 me
 010 you
 011 we
 100 they

 101 he
 110 she
 111 yah
 000 nay

Mandelbrot Set Zoom

 I just got through doing a video showing a zoom into a Mandelbrot Set which can be seen here on YouTube. There seems to have been some loss in the quality of the images during the upload process and I will see what I can do about that. I have also posted better stills from the zoom on Picasa.

Favorite Limerick

Relativity

There was a young lady named Bright
Whose speed was far faster than light;
 She set out one day,
 In a relative way
And returned on the previous night.

Published anonomously by A. H. Reginald Buller
in Punch, 19 Dec, 1923.