What's special about 71556319?

CRGreathouse

Forum Staff
Nov 2006
16,046
936
UTC -5
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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mathbalarka

Math Team
Mar 2012
3,871
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India, West Bengal
Just wondering: Does the growth of the denominators in the greedy expansion of some transcendental depends on its transcendence measure?
 
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CRGreathouse

Forum Staff
Nov 2006
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I don't think so. You'd expect about that much growth from any number.
 
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v8archie

Math Team
Dec 2013
7,712
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Colombia
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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