title: Generate very very large random numbers
body: <p>How would you generate a very very large random number? I am thinking on the order of 2^10^9 (one billion bits). Any programming language -- I assume the solution would translate to other languages.</p>
  
  <p>I would like a uniform distribution on [1,N].</p>
  
  <p>My initial thoughts:</p>
  
  <p>--You could randomly generate each digit and concatenate. Problem: even very good pseudorandom generators are likely to develop patterns with millions of digits, right?</p>
  
  <ul>
  <li><p>You could perhaps help create large random numbers by raising random numbers to random exponents. Problem: you must make the math work so that the resulting number is still random, and you should be able to compute it in a reasonable amount of time (say, an hour).</p></li>
  <li><p>If it helps, you could try to generate a possibly non-uniform distribution on a possibly smaller range (using the real numbers, for instance) and transform. Problem: this might be equally difficult.</p></li>
  </ul>
  
  <p>Any ideas?</p>