Mathematics - Number Theory - Analytic number theory - Explore Prime Distributions

The student explores prime patterns computationally. Prompts: (1) 'Compute π(x)/[x/ln(x)] for x=100, 1000, 10000, 100000. Does it approach 1?' (2) 'Plot the gaps between consecutive primes up to 1000. Are they getting larger on average?' (3) 'Twin primes (p, p+2): list all under 100. Do they seem to