20130216, 18:28  #1 
Feb 2013
2^{2}×7 Posts 
Mills' Primes, Mills' Constant
http://en.wikipedia.org/wiki/Mills'_constant
http://mathworld.wolfram.com/MillsConstant.html I searched for a thread on this. There doesn't appear to be one. A guy named William Mills proved in the 1940s that: there exists a real number, A, such that (A^(3^n)) is prime for all 'n'. It turns out there are many of these numbers, but Mill's Constant is defined as the least of all of these at about: 3.306XXXX>>>> (Infinity?) The trouble is, no one knows if A is even rational, or what it is, and the only way (now) to extend the number of known decimal places is to have the prime A^(3^n) makes, in order to generate A. Thoughts? Last fiddled with by ewmayer on 20130216 at 19:44 Reason: "Crandall & Pomerance is your friend"  proving such a constant exists is alas of practical uselessness, AFAWK. 
20130217, 22:22  #2 
Nov 2012
Canada
21_{10} Posts 
Mills
EWMayer is acknowledged for his assistance in the book alluded to in the `fiddled with` section. Take a good hard look through that first then you may not need to ask your question.

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Mills prime and Mersenne  firejuggler  Miscellaneous Math  5  20170510 16:28 
CopelandErdos Constant Primes  rogue  And now for something completely different  32  20160620 01:55 
Mills' primes  CRGreathouse  Computer Science & Computational Number Theory  15  20130728 17:07 
Constant n Search  kar_bon  Riesel Prime Data Collecting (k*2^n1)  5  20090622 23:00 
Constant nSearch for k*2^n1  kar_bon  Riesel Prime Search  45  20071127 19:15 