If we look at the number of twin primes less than
x we see the usual irregularities associated
with distributions of primes:
but back up and look again and the distribution looks much smoother:
Hardy and Littlewood conjectured that there are about
twin primes less than or equal to x where the infinite product is the twin prime constant. See the page "a simple heuristic" linked below for information on how this conjecture is formed.
This constant was estimated by Wrench and others to be approximately 0.6601618158...
Related pages (outside of this work)