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 Mills[1]. Although Mills' constant itself is not a large number, it generates a sequence of prime numbers which grows faster than the exponential function.

Decimal expansion

The decimal expansion of Mills constant is given as

\begin{eqnarray*} 1.30637788386308069046861449260260571291678458515671364436805375996643405376682659882150140370119739570729 \ldots \end{eqnarray*}

under Riemann Hypothesis.[2]


Primes

Here is a list of the first few terms in the sequence of primes generated by Mills' constant:[1]

  • 2
  • 11
  • 1361
  • 2521008887
  • 16022236204009818131831320183
  • 4113101149215104800030529537915953170486139623539759933135949994882770404074832568499


See also

Sources

  1. 1.0 1.1 A051254 in OEIS.
  2. A051021 in OEIS.
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