visualizationsprime relationships in arbitrary 2-dimensional space
varios 2-dimensional grids of prime numbers, denoted as points. the nearest neighbor relationships are denoted by lines between the points. parameters are denoted in the filenames which are number of dimensions, the x and y values, and the nearest neighbor level. these images also exhibit a small bug in the nearest neighbor search code.2d_100_100_nns_3
2d_100_100_nns_4
2d_100_100_nns_5
distribution of goldbach pair counts
distribution of strong goldbach pair counts for all primes up to 10,000. the pair counts are denoted in red. pi(N) is purple (the actual count of primes up to and including n), the approximation of pi(N), n/log n, is in green, and and pi(n)/log pi(n) is yellow. the latter appears to follow the average curve of the distribution of goldbach pair counts, but appears to diverge farther out. sgc_10000
programmatic prime mapping in 2-dimensions
various programmatic mappings of primes numbers using xplot graphing and SDL. different properties are used to vary the step lengths and direction of lines. examples being the number of goldbach pairs at p+1, the number of non-primes between two primes, iterative and cumulative stepping, directions changes by way of modulo, direction changes based on least significant nibble of p, among others. more detail available soon, as i plan on redesigning this particular page to include more information on how the images were generated. 4w-bw-m-100k
4w-bw-ml-100k
4w-bw-ps-19k
4w-bw-ps-100k
4w-cps-10k
4w-cps-100k
4w-density-1m
4w-gb-10k
4w-gb-100k
4w-iterative-10k
4w-iterative-100k
4w-mod-int-100k
8w-iterative-10k
8w-iterative-100k
linear-gb-density
zeta function arguments and results in 2-dimensions
available soon
prime relationships in arbitrary 3-dimensional space
available soon
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