Book ChapterDOI
The Prime Divisor Functions
Manfred R. Schroeder,Manfred R. Schroeder +1 more
- pp 135-148
TLDR
In this paper, the authors consider only prime divisors of n and ask, for given order of magnitude of n, how many prime factors are there typically and how many different ones are there?Abstract:
Here we consider only prime divisors of n and ask, for given order of magnitude of n, “how many prime divisors are there typically?” and “how many different ones are there?” Some of the answers will be rather counterintuitive. Thus, a 50-digit number (1021 times the age of our universe measured in picoseconds) has only about 5 different prime factors on average and — even more surprisingly — 50-digit numbers have typically fewer than 6 prime factors in all, even counting repeated occurrences of the same prime factor as separate factors.read more
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Journal ArticleDOI
Handbook of Mathematical Functions
Book
An Introduction to the Theory of Numbers
TL;DR: The fifth edition of the introduction to the theory of numbers has been published by as discussed by the authors, and the main changes are in the notes at the end of each chapter, where the author seeks to provide up-to-date references for the reader who wishes to pursue a particular topic further and to present a reasonably accurate account of the present state of knowledge.