Standard WolframAlpha doesn't conclude whether below sum converges or diverges
sum(prime(n)/prime(n+1)/n^2,n=1...infinity)
Using Maple notation for the input to Inverse Symbolic Calculator
evalf[16](sum(nextprime(p)/nextprime(nextprime(p))/p^2, p = 1 .. 1000000));
gives 1.116727203339173
