The Hardy-Ramanujan theorem is a result in number theory, proved by Srinivasa Ramanujan and checked by G. H. Hardy, stating that the normal order of the number of distinct prime factors of a number n is the logarithm of the logarithm of n. Roughly speaking, this means that most numbers have approximately this many distinct prime factors. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
Classification
Statement Form StatementThe normal order of the number of distinct prime factors of n is log log n. 1 Connections
Has Statement Form
In Branch
Source Wolfram MathWorld: Hardy-Ramanujan Theorem
Proved By
Source Hardy-Ramanujan theorem (Wikipedia)
Sources
1. Hardy-Ramanujan theorem (Wikipedia)
Introduction, first sentence
the normal order of the number
Proved By: Srinivasa Ramanujan, Lead paragraph
proved by Ramanujan and checked by Hardy
View the SourceWolfram MathWorld: Hardy-Ramanujan Theorem
Wolfram MathWorldIn Branch: Number Theory, Subject classificationsQuote, In Branch: Number Theory, Subject classifications
Number Theory Prime Numbers
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