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I assumed $p_n=nlogn$ and evaluated the convergence using cauchy's condensation test and got the series divergent. Is my answer correct?

Aabhas Vij
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  • Also: https://math.stackexchange.com/q/120592, https://math.stackexchange.com/q/15946 – Martin R May 08 '19 at 06:50
  • The intuition that $p_n$ behave somewhat similar to $n \log n$ indeed hints that the prime harmonic series $\sum_{n\geq1} 1/p_n$ will diverge, but this is by no means a proof. – Sangchul Lee May 08 '19 at 06:51
  • https://en.wikipedia.org/wiki/Divergence_of_the_sum_of_the_reciprocals_of_the_primes – Martin R May 08 '19 at 06:52
  • Oh thanks a lot! This clarifies a lot of things! But can my proof be stated incorrect? – Aabhas Vij May 08 '19 at 06:54

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