What is the limit of the sum of the reciprocals of all primes? (1/2 + 1/3 + 1/5 + 1/7 ...)

Question

chaise · Answer

There are is an infinite number of primes and therefore you cannot find the sum of the reciprocals of all primes.

anonymous · Answer

Not a good answer Champion...  An infinite series can have a limit, any geometric series with ratio <1 converges to a limit, and yet has an infinite number of terms.  
The sum of the reciprocal primes diverges, so it has no limit.  This was shown first by Leonhard Euler.  He used the Zeta function for the proof.  Look it up.

chaise · Answer

Should I rephrase it - there is an unknown number of prime numbers and therefore the sum of all the reciprocals of prime numbers cannot be known.

chaise · Answer

I guess you cannot really know the limit to a high precision, but I assume it would be 2 or 3, somewhere in the middle, atleast to the millionth term.