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June 20th, 2014, 06:17 AM   #1
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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.
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June 21st, 2014, 06:56 AM   #2
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Just wondering: Does the growth of the denominators in the greedy expansion of some transcendental depends on its transcendence measure?
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Last edited by skipjack; November 19th, 2014 at 02:32 AM.
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June 22nd, 2014, 07:50 AM   #3
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I don't think so. You'd expect about that much growth from any number.
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June 22nd, 2014, 09:07 AM   #4
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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?
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June 22nd, 2014, 09:45 AM   #5
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Quote:
Originally Posted by v8archie View Post
Are you saying that it's the first non-consecutive prime reciprocal in the expression?
Yes.
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