MILLS' CONSTANT

In mathematics, 'Mills' constant' is defined as the smallest positive real number ''A''; such that the integer part
:$lfloor\; A^\{3^\{n\}\};$
floor
is a prime number, for all positive integers ''n''. Its value is approximately
: (Sloane's A051021).
In 2005, Chris Caldwell and Yuanyou (Fred) Cheng computed almost seven thousand base 10 digits of Mills' constant under the assumption that the Riemann hypothesis is true. It is hard to calculate Mills' constant accurately (although several thousand digits are known), because to do that with the current state of knowledge one needs to know the primes it generates. There is no formula for this number as of now, and it is not even known if this number is rational. It is known, however, that the first few primes generated (the so-called 'Mills primes') are 2, 11, 1361, 2521008887... .
This constant is named after W. H. Mills who proved in 1947 the existence of θ based on results of Hoheisel and A. E. Ingham on the gaps between the primes.

Contents

See also

References

External link

See also

★ Formula for primes

References

★ Caldwell, Chris K. and Cheng, Yuanyou (Fred) "Determining Mills' Constant and a Note on Honaker's Problem." ''Journal of Integer Sequences'' Vol. 8 (2005), article 05.4.1. http://www.cs.uwaterloo.ca/journals/JIS/VOL8/Caldwell/caldwell78.html

External link

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