## Generalised prime systems with periodic integer counting functionTools
Hilberdink, T.
(2012)
To link to this article DOI: 10.4064/aa152-3-1 ## Abstract/SummaryWe study generalised prime systems (both discrete and continuous) for which the `integer counting function' N(x) has the property that N(x) ¡ cx is periodic for some c > 0. We show that this is extremely rare. In particular, we show that the only such system for which N is continuous is the trivial system with N(x) ¡ cx constant, while if N has finitely many discontinuities per bounded interval, then N must be the counting function of the g-prime system containing the usual primes except for finitely many. Keywords and phrases: Generalised prime systems. I
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