Thread: Predict M47 View Single Post
 2008-11-03, 03:01 #47 cheesehead     "Richard B. Woods" Aug 2002 Wisconsin USA 170148 Posts Hmmm ... yes, a bit of similarity in runs of initial decimal digits: ... 607 1279 2203 2281 3217 4253 4423 9689 ... 6972593 13466917 20996011 24036583 25964951 30402457 32582657 37156667 43112609 (?) But why should that mean anything other than a coincidence within a larger demonstration of Benford's Law (http://mathworld.wolfram.com/BenfordsLaw.html or http://en.wikipedia.org/wiki/Benford's_law) over a set of numbers (_all_ known Mersenne-prime exponents, not just two specially-picked subsets) whose distribution is expected to be related to logarithms? Looking at all the known Mersenne-prime exponents with 1-7 decimal digits (we don't yet have a complete census for 8-decimal-digit exponents), the counts by initial digit are: 1: 12 2: 7 3: 4 4: 3 5: 2 6: 3 7: 2 8: 3 9: 2 Of the 38 exponents in that range, 12/38 = 32% start with "1", 7/38 = 18% start with "2", 4/38 = 11% start with "3". Compare that to the ideal Benford distribution of 30.1% "1"s, 17.6% "2"s, and 12.5% "3"s. Pretty close for such a small sample (N = 38), eh? And -- Benford's Law comes with a logical mathematical explanation -- no guessing needed! Last fiddled with by cheesehead on 2008-11-03 at 03:50