real analysis - Is $sum_{n=1}^{+ infty}left(frac {1}{n}-frac{1}{p_n}right)$ convergent?

It is known that $$\sum_{n=1}^{+ \infty} \frac {1}{n}$$ is divergent. Also, it is known that $$\sum_{n=1}^{+ \infty} \frac {1}{p_n}$$ is divergent where $p_n$ is $n$-th prime number.

I was thinking what would happen (in the sense of convergence) if we termwise subtract these two series to obtain $$\sum_{n=1}^{+ \infty} \left(\frac {1}{n}-\frac{1}{p_n}\right)$$

Is $$\sum_{n=1}^{+ \infty} \left(\frac {1}{n}-\frac{1}{p_n}\right)$$ convergent?