Abstract
We discuss cyclic reciprocal sums of products of primes that appear in distributions of no-prime (NP) sequences. Formulas and asymptotics for cyclic sums of arbitrary order are obtained, and possible connections with certain fields of physics briefly discussed.



![Author ORCID: We display the ORCID iD icon alongside authors names on our website to acknowledge that the ORCiD has been authenticated when entered by the user. To view the users ORCiD record click the icon. [opens in a new tab]](https://www.cambridge.org/engage/assets/public/coe/logo/orcid.png)