Prime numbers on the nose

The Prime Number Theorem gives the following asymptotic for the n-th prime: p_n ~ iL(n) ~ n log n, where we are calling iL the inverse to the logarithmic integral function, Li. We call p a prime "on the nose" if p=[iL(n)] for some n, i.e. these are the primes which exactly equal their expected value. We will describe recent work on the number of primes on the nose less than a given bound.

Alex Kontorovich