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 June 20th, 2014, 06:17 AM #1 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms What's special about 71556319? 1/2 + 1/3 + 1/5 + ... + 1/54617881 + 1/71556319 + 1/640488930211807 + 1/31479896620985421014853629981 + ... = $\pi.$ This is the greedy representation of $\pi$ as a sum of prime reciprocals. The ellipsis represents the 3260801 primes between 5 and 54617881; 71556319 is the first prime outside that block. I considered asking this as an unfair question at the Q&A thread but thought it would be better to post it separately. Thanks from ZardoZ, mathbalarka and eddybob123
 June 21st, 2014, 06:56 AM #2 Math Team     Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Just wondering: Does the growth of the denominators in the greedy expansion of some transcendental depends on its transcendence measure? Thanks from eddybob123 Last edited by skipjack; November 19th, 2014 at 01:32 AM.
 June 22nd, 2014, 07:50 AM #3 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms I don't think so. You'd expect about that much growth from any number. Thanks from eddybob123
 June 22nd, 2014, 09:07 AM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,690 Thanks: 2669 Math Focus: Mainly analysis and algebra I still don't see why that should make it special. The block you site looks fairly arbitrary. Are you saying that it's the first non-consecutive prime reciprocal in the expression? Thanks from eddybob123
June 22nd, 2014, 09:45 AM   #5
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Quote:
 Originally Posted by v8archie Are you saying that it's the first non-consecutive prime reciprocal in the expression?
Yes.

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