This is a graph of all the semiprimes with 7 as a prime factor, up to 4333. Semiprimes are on the x-axis. The number of digits in the sequence until it repeats (e.g. 1/7=0.142857142857 has 6 digits until the sequence repeats) is on the y-axis.
Numbers on the green line, follow route 2, i.e. if you add one you get a prime factor. Numbers above the green line follow route 1. Numbers below the green line follow route 3.
These appear random, but they are not.
Here’s the graph of the semiprimes with 7 as a prime factor, compared to the graphs of semiprimes with 13 as a prime factor.
7
13
The slopes of the lines are multiples of the inverse of one of the prime factors(i.e. 4/7).
Copyright 2016 DeGroff
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