Valentin's recent challenge involving the harmonic series caused me to run across a related series:

http://mathworld.wolfram.com/HarmonicSeriesofPrimes.html

and a fascinating modification to it.

If you delete from the harmonic series of primes those primes that contain each of the digits 0,1,2,3,4,5,6,7,8,9 at least once, the series converges.

A paper providing a proof of this was published in Mathematics Magazine in October, 1995.

But, the author didn't provide the value of the limit.

Can we find it with our calculators?