and the integral logarithm of
does in fact become infinite of an order not greater than
in
.[21] Further, we should determine whether the occasional condensation of prime numbers which has been noticed in counting primes is really one to those terms of Riemann's formula which depend upon the first complex zeros of the function
.
After an exhaustive discussion of Riemann's prime number formula, perhaps we may sometime be in a position to attempt the rigorous solution of Goldbach's problem,[22] viz., whether every integer is expressible as the sum of two positive prime numbers; and further to attack the well-known question, whether there are an infinite number of pairs of prime numbers with the difference