@article {17547, title = {A note on the distribution of the number of prime factors of the integers}, journal = {Information Processing Letters}, volume = {109}, year = {2008}, month = {2008/12/31/}, pages = {133 - 135}, abstract = {The Chernoff{\textendash}Hoeffding bounds are fundamental probabilistic tools. An elementary approach is presented to obtain a Chernoff-type upper-tail bound for the number of prime factors of a random integer in { 1 , 2 , {\textellipsis} , n } . The method illustrates tail bounds in negatively-correlated settings.}, keywords = {Chernoff bounds, Dependent random variables, Primes, Probabilistic number theory, randomized algorithms, Tail bounds}, isbn = {0020-0190}, doi = {10.1016/j.ipl.2008.09.010}, url = {http://www.sciencedirect.com/science/article/pii/S0020019008002688}, author = {Srinivasan, Aravind} }