I was watching a video lecture (in Italian by the Italian logician Piergiorgio Odifreddi; if you know Italian you can watch it here) about the solitude of prime numbers, which is also the title of a famous Italian novel "La solitudine dei numeri primi" (which I've not read yet) by Paolo Giordano.
Many reasonings in this video lecture are based on the fact that, if we have a set $A$ of numbers $a_1, a_2, ...$, trying to sum their reciprocals and analysing after that the finiteness of the result should tell us about the solitude of the numbers in the original set $A$.
What exactly is meant by the solitude of a set of numbers, in this case the set of prime numbers?
Why the finiteness of the result of the sum of the reciprocals of these numbers, in the case above, the sum would be $\frac{1}{a_1} + \frac{1}{a_2} + ...$, should tell us about the solitude of the numbers in $A$?
At a certain point during the talk actually talking about "solitude of prime numbers" is not that correct. I've not finished watching it...