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/
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Statement Form StatementThe normal order of the number of distinct prime factors of n is log log n. 1 Connections
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In Branch
Source Wolfram MathWorld: Hardy-Ramanujan Theorem
Principal Result Of
Source Hardy-Ramanujan Theorem (Wikipedia)
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 SourceHardy-Ramanujan Theorem (Wikipedia)
Principal Result Of: G. H. Hardy, Lead sentence of the article on the resultQuote, Principal Result Of: G. H. Hardy, Lead sentence of the article on the result
In mathematics, the Hardy-Ramanujan theorem, proved by Ramanujan and checked by Hardy states that the normal order of the number ω ( n ) {\displaystyle \omega (n)} of distinct prime factors of a number n {\displaystyle n} is log log n {\displaystyle \log \log n} .
Wolfram 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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