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Old 2013-02-16, 18:28   #1
Andrew's Avatar
Feb 2013

22×7 Posts
Default Mills' Primes, Mills' Constant'_constant

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.


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.
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Old 2013-02-17, 22:22   #2
Nov 2012

2110 Posts
Default 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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