most recent 30 from http://mathoverflow.net 2013-05-22T19:34:34Z http://mathoverflow.net/feeds/user/13723 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/11934/magnitude-of-grahams-number/58765#58765 Kevin 2011-03-17T15:41:33Z 2011-03-17T15:41:33Z

<p>Here's one way to put it:</p> <p>3↑↑3 = 3^(3^3) ~= 7.6 trillion</p> <p>3↑↑↑3 = 3↑↑(3↑↑3) = 3↑↑(7.6 trillion). Let's start calculating this number:</p> <p>3↑↑4 = 3^(7.6 trillion) ~= 10^(3.6 trillion) > a google</p> <p>3↑↑5 = 3^(10^3.6 trillion) ~= 10^(0.477 * 10^3.6 trillion) > a googleplex</p> <p>3↑↑6 > a googleplexian.</p> <p>Now - take this to the 7.6 trillionth power of 3. 3↑↑↑3 makes a gooogleplexian look like bus fare.</p> <p>G1 = 3↑↑↑(3↑↑↑3).</p> <p>And G2 = 3↑(G1 times)3</p> <p>G1 is ridiculously large, and it just gets worse from there.</p>