>>13635357I was reading the "Prime number sieves" book and it was mentioned that the probability of a particular number being prime is $1/\pi(n)$.
Then I tried to do a numerical experiment to find out if that was true, i.e., I ran two loops (one for odd primes, the other for even primes) and checked if the sum was prime, and plotted the result. The result was that for every number up to $2^32^32^32^32^4=1.1\times 10^{17}$, the number is prime with probability $1/\pi(n)$, but as you reach $2^{64}$, the probability drops off very quickly.
