Abstract
The primorial of a prime is the product of all primes . Let denote the largest prime with , where is Euler’s totient function. We show that the normal order of is ; that is, as on a set of integers of asymptotic density 1. In fact, we show there is an asymptotic secondary term and, on a tertiary level, there is an asymptotic Poisson distribution. We also show an analogous result for the largest integer with .
Citation
Paul Pollack. Carl Pomerance. "Phi, primorials, and Poisson." Illinois J. Math. 64 (3) 319 - 330, September 2020. https://doi.org/10.1215/00192082-8591576
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