Saturday, 5 November 2011

The grid of n-factor numbers

So in the previous post I showed a grid of composite numbers of the form 6n+/-1, and also looked at the problem of using it to look at prime patterns.

What I tried next isn't a complete solution to this problem, but I think it brings a bit more clarity to the grid and makes it more visually useful. Instead of the slightly confusing overlaying of rectangles of n-multiples, I used a different colour scheme, and graded the numbers according to how many factors they have. In this image, prime numbers are pink, semi-primes (numbers with 2 factors such as 25, 35, 49, 55 etc) are yellow, 3-factor numbers are green, 4-factor numbers are blue, 5-factor numbers are red, and the one 6-factor number (21875) is purple. (I've only shown the (6n+1)(6n-1) region, but this pattern would extend over the whole grid.)

We still see a similarly fractal pattern starting to emerge. In the next post I will talk about the distribution of semi-primes on this grid, and what we can know about how it will develop.

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