Abstract
In this paper we introduce a degree of primality for natural numbers, and hence, a measure of primality for intervals of consecutive numbers. We characterize maximally prime intervals of length $\le 3$ and their primalities. Maximally prime intervals of length 2 are those that contain Mersenne or Fermat primes; maximally prime intervals of length 3 are, but for a few exceptions, those whose midpoints are Dan numbers. There are relatively few maxprimes for larger lengths. We present a heuristic argument for an asymptotic form describing the distribution of maximal primalities. Finally, we mention open problems and directions for further research.
Citation
Joseph Pe. "On a Degree of Primality." Missouri J. Math. Sci. 23 (2) 159 - 172, October 2011. https://doi.org/10.35834/mjms/1321045144
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