The other day my friend noticed that for the first several pairs of consecutive integers, the difference of their cubes was prime. I investigated the subject and am posting the Mathematica file to test CDF compatibility with the blog.
Well wordpress.com is retarded and claims that embedding is not allowed “for security reasons”, so I guess I just have to link all my Mathematica work.
What it came down to, in case anyone was wondering, is explained by the graph above. The horizontal axis is in 100s of numbers, the vertical axis is the percentage of those numbers that are prime. The red curve corresponds to the percentage of the odd integers which are prime (up to the first 1,000,000) and the blue curve is the percentage of the numbers generated by the difference of cubes of sequential integers which are prime (up to the first 1,000,000). There doesn’t seem to be anything special about the difference of cubes of sequential integers with regards to primality. Further explanation is in the link.