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- Hardy–Ramanujan_theorem abstract "In mathematics, the Hardy–Ramanujan theorem, proved by Hardy & Ramanujan (1917), states that the normal order of the number ω(n) of distinct prime factors of a number n is log(log(n)). Roughly speaking, this means that most numbers have about this number of distinct prime factors.A more precise version states that for any real-valued function ψ(n) that tends to infinity as n tends to infinityor more traditionallyfor almost all (all but an infinitesimal proportion of) integers. That is, let g(x) be the number of positive integers n less than x for which the above inequality fails: then g(x)/x converges to zero as x goes to infinity.A simple proof to the result Turán (1934) was given by Pál Turán, who proved that The same results are true of Ω(n), the number of prime factors of n counted with multiplicity.This theorem is generalized by the Erdős–Kac theorem, which shows that ω(n) is essentially normally distributed.".
- Hardy–Ramanujan_theorem wikiPageID "14743376".
- Hardy–Ramanujan_theorem wikiPageRevisionID "586001866".
- Hardy–Ramanujan_theorem first "A.".
- Hardy–Ramanujan_theorem id "H/h110080".
- Hardy–Ramanujan_theorem last "Hildebrand".
- Hardy–Ramanujan_theorem subject Category:Analytic_number_theory.
- Hardy–Ramanujan_theorem subject Category:Theorems_about_prime_numbers.
- Hardy–Ramanujan_theorem comment "In mathematics, the Hardy–Ramanujan theorem, proved by Hardy & Ramanujan (1917), states that the normal order of the number ω(n) of distinct prime factors of a number n is log(log(n)). Roughly speaking, this means that most numbers have about this number of distinct prime factors.A more precise version states that for any real-valued function ψ(n) that tends to infinity as n tends to infinityor more traditionallyfor almost all (all but an infinitesimal proportion of) integers.".
- Hardy–Ramanujan_theorem label "Hardy–Ramanujan theorem".
- Hardy–Ramanujan_theorem label "Теорема Харди — Рамануджана".
- Hardy–Ramanujan_theorem sameAs Hardy%E2%80%93Ramanujan_theorem.
- Hardy–Ramanujan_theorem sameAs Q5656674.
- Hardy–Ramanujan_theorem sameAs Q5656674.
- Hardy–Ramanujan_theorem wasDerivedFrom Hardy–Ramanujan_theorem?oldid=586001866.