User david willis - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T04:22:37Z http://mathoverflow.net/feeds/user/8826 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/36897/probabilistic-interpretation-of-prime-number-theorem Probabilistic interpretation of prime number theorem David Willis 2010-08-27T16:13:38Z 2010-09-01T15:40:46Z <p>Suppose there is a function f(x) which is the "probability" that the integer x is prime. The integer x is prime with probability f(x), and then divides the larger integers with probability 1/x; so as x changes from x to x+1, f(x) changes to (roughly)</p> <pre><code>f(x).(1-f(x)/x). </code></pre> <p>How do I show that? I can go on to show</p> <p>df/dx +f^2/x=0</p> <p>and thus 1/(logx +c) is solution but I can't show that step on how f(x) changes. please advise</p> http://mathoverflow.net/questions/37253/trying-to-sum-a-series-related-to-catalan-numbers-perhaps Trying to sum a series (related to catalan numbers perhaps) David Willis 2010-08-31T11:52:42Z 2010-08-31T12:04:23Z <p>Whilst trying to solve a combinatorics problem I am faced with summing this series:</p> <p>1+ 2C_1 2/(3^2) + 4C_2 (2^2)/(3^4) + 6C_3 (2^3)/(3^6)+ ... + 2nC_n (2^n)/(3^(2n))+...</p> <p>Where 4C_2 is 4 choose 2.</p> <p>Any idea how to approach this problem?</p> http://mathoverflow.net/questions/36897/probabilistic-interpretation-of-prime-number-theorem/36902#36902 Comment by David Willis David Willis 2010-08-27T17:12:03Z 2010-08-27T17:12:03Z Wow. Smart guy. Thanks.