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September 24th, 2007, 05:31 PM  #1 
Senior Member Joined: Dec 2006 Posts: 1,111 Thanks: 0  An unusual prime number question
Suppose that we took all the prime numbers (in whatever base we were working with) and wrote them all down in a row, with a decimal point at the beginning. In other words: 0.23571113171923... Would the resulting number be irrational (and thus nonconstructable)? Would it also be transcendental? 
September 24th, 2007, 07:36 PM  #2 
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 
This is the Copeland–Erdős constant. It is base10 normal, and as such irrational. I don't think its transcendence has been proved, but surely no one doubts it  think about the consequences of showing that it's algebraic! 
September 25th, 2007, 05:28 AM  #3  
Senior Member Joined: Dec 2006 Posts: 1,111 Thanks: 0  Quote:
 
September 25th, 2007, 05:46 AM  #4  
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  Quote:
 
September 25th, 2007, 07:51 AM  #5  
Senior Member Joined: Dec 2006 Posts: 1,111 Thanks: 0  Quote:
 
September 25th, 2007, 08:02 AM  #6  
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  Quote:
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