Journal of Integer Sequences, Vol. 24 (2021), Article 21.9.5

Sum of Reciprocals of Germain Primes

Samuel S. Wagstaff, Jr.
Center for Education and Research in Information Assurance and Security
Department of Computer Sciences
Purdue University
West Lafayette, IN 47907-1398


A prime p is a Germain prime if 2p + 1 is also prime. We compute the sum of the reciprocals of the Germain primes and related sequences. Since we do not know whether there are infinitely many Germain primes, all we can do is bound the sum in an interval.

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(Concerned with sequences A001097 A005384 A023212 A023228.)

Received August 16 2021; revised version received October 2 2021. Published in Journal of Integer Sequences, October 2 2021.

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