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 2013-02-16, 18:28 #1 Andrew     Feb 2013 22×7 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 2013-02-16 at 19:44 Reason: "Crandall & Pomerance is your friend" - proving such a constant exists is alas of practical uselessness, AFAWK.
 2013-02-17, 22:22 #2 ishkibibble   Nov 2012 Canada 2110 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.

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