A Prime Discussion

Last week, I met a former colleague, who is now working in risk management of an Austrian bank. It was a very enjoyable evening with a few beers and memories of the times when we were undergraduate students.

This obviously (at least for mathematicians) led us to prime numbers.

So, today's question:
Does the harmonic series of prime numbers, i.e.,

 converge?

I will sketch a proof (whether it converges or not) next week.

Although prime numbers seem to belong to pure mathematics, there are at least two important applications in finance: one is for encrpyting information by the RSA algoithm, the other one is for generating low discrepancy numbers.