Does this prime sum converge?

It is well-known that n=11n=1+12+13+14+...\displaystyle \sum_{n=1}^{\infty} \frac{1}{n} = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + ... diverges. But how about the sum below?

p prime1p=12+13+15+17+... \displaystyle \sum_{p \text{ prime}} \frac{1}{p} = \frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{7} + ...

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