I over heard Peter asking about how frequently prime numbers occur, specifically, are they less frequent as numbers get bigger. This made me curious. In the graph below, each data point represents the count of prime numbers between successive groupings of 1000 numbers. Thus the first data point is the count of prime numbers occurring between 0 and 1000, the second data point the count between 1001 and 2000, and so on. The data was generated with a fairly simple bash for loop using the bsd-games primes command:
m=1000; for i in ``seq 0 $m 1000000``; do j=$(( $i+$m )); k=``primes $i $j | wc -l``; echo "$j $k" >> input.dat; done
