Mills' constant

Mills' constant is the smallest positive real number \(A\) such that \(\lfloor A^{3^n} \rfloor\) is a prime number for any natural number \(n\), and its existence was proven by MillsWilliam H. Mills, A prime-representing function, Bull. Amer. Math. Soc., Vol. 53, No. 6 (1947), p. 604. PDF; Errata, ibid., Vol. 53, No 12 (1947), p. 1196.Chris K. Caldwell and Yuanyou Chen, Determining Mills' Constant and a Note on Honaker's Problem, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.1.A051254 in OEIS.. Mills' constant generates a sequence of prime numbers which grows faster than the exponential function.
== Decimal expansion ==
The Mills' constant begins with the following 600 digits
under Riemann Hypothesis.
== Primes ==
Here is a list of the first few terms in the sequence of primes generated by Mills' constant:Allam's Numbers It's Prime Time! Retrieved 2024-09-12.
* 2
* 11
* 1361
* 2521008887
* 16022236204009818131831320183
* 
* 
== See also ==
* Prime numbers
* Numbers in number theory
* Wright's primes
== Sources ==
Category:Numbers
Category:Prime numbers
Category:Exponential growth rate
ja:ミルズの定理
Category:Numbers with peer-reviewed source