# Ulam Spirals in R and ggplot

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Having seen a twitter post speed by about Ulam Spirals I started to read up. As the story goes in 1963 Stanislaw Ulam was bored at conference and started scribbling numbers in a spiral. What he discovered was a strange diaginal pattern of Prime Numbers. I was a little bored as well, so i decided to write up some R to plot these patterns.

Here is the main function. I am sure there are more elegant ways of calculating a Ulam spiral but here is my hack. First we calculate the diagonals and then fill in the gaps.

Ulam.Spiral

Here is the output for a 5X5 spiral

[,1] [,2] [,3] [,4] [,5] [1,] 17 16 15 14 13 [2,] 18 5 4 3 12 [3,] 19 6 1 2 11 [4,] 20 7 8 9 10 [5,] 21 22 23 24 25

The code is on git hub. https://github.com/jofusa/ulam-spirals-R

Many Thanks to http://librestats.wordpress.com/2011/08/20/prime-testing-function-in-r/ for a useful IsPrime() function and saving me some time.

Here is an example Plot- Prime Number are in red:

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