It is possible, by means of zeta function regularization and the Ramanujan summation method, to assign a finite value to the sum of the natural numbers (here $n \to \infty $) :
$ 1 + 2 + 3 + 4 + \cdots + n \; {“ \;=\; ”} - \frac{1}{12} . $
Is it also possible to assign a value to the sum of primes, $ 2 + 3 + 5 + 7 + 11 + \cdots + p_{n} $ ($n \to \infty$) by using any summation method for divergent series?
This question is inspired by a question on quora.
Thanks in advance,