PRintervallum
PRintervallum is a term used in recreational and analytic number theory to denote a class of intervals on the integers that are defined by containing a prescribed number of prime numbers. The abbreviation PR is taken from prime, and intervallum is Latin for interval. The concept is employed in discussions of prime distribution and prime gaps, and it is often used in puzzle contexts as well as in heuristic investigations.
For an integer r ≥ 1, a PRintervallum of order r is an open interval (a, b) with
The interval (1, 4) contains the primes 2 and 3, so it is a PRintervallum of order
The function L(r) is not fixed for all r and is studied both for its intrinsic interest
The term PRintervallum emerged in online recreational and mathematical literature in the early 2010s and has