I have read many a wonderful proof that the sum of the reciprocals of the primes is divergent and I know that the sum of the reciprocals of twin primes does not diverge, but do we know any results concerning the sum of the reciprocals of Ramanujan primes?
2026-03-27 15:10:35.1774624235
Is the sum of the reciprocals of Ramanujan primes divergent?
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The divergence follows from the bounds $2n\ln2n < R_n < 4n\ln4n$ (see https://en.wikipedia.org/wiki/Ramanujan_prime).