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A051254 Mills primes. 12
2, 11, 1361, 2521008887, 16022236204009818131831320183, 4113101149215104800030529537915953170486139623539759933135949994882770404074832568499 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Mills showed that there is a number A > 1 but not an integer, such that floor( A^(3^n) ) is a prime for all n = 1, 2, 3, ... A is approximately 1.306377883863... (see A051021).

Obverse of this is A118910 a(1) = 2; a(n) is greatest prime < a(n-1)^3. - Jonathan Vos Post, May 05 2006

REFERENCES

T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 8.

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..8

Chris K. Caldwell, Mills' Theorem - a generalization

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.

S. R. Finch, Mills' Constant

Brian Hayes, Pumping the Primes, bit-player, 19 August 2015.

W. H. Mills, A prime-representing function, Bull. Amer. Math. Soc., Vol. 53 (1947), p. 604.

Eric Weisstein's World of Mathematics, Mills' Prime

Eric Weisstein's World of Mathematics, Prime Formulas

Eric W. Weisstein, Table of n, a(n) for n = 1..13

FORMULA

a(1) = 2; a(n) is least prime > a(n-1)^3. - Jonathan Vos Post, May 05 2006

EXAMPLE

a(3) = 1361 = 11^3 + 30 = a(2)^3 + 30 and there is no smaller k such that a(2)^3 + k is prime. - Jonathan Vos Post, May 05 2006

a(4) = 16022236204009818131831320183 = a(3)^3 + 80 = 2521008887^3 + 80 and there is no smaller k such that a(3)^3 + k is prime. - Jonathan Vos Post, May 05 2006

MAPLE

floor(A^(3^n), n=1..10); # A is Mills's constant: 1.306377883863080690468614492602605712916784585156713644368053759966434.. (A051021).

MATHEMATICA

p = 1; Table[p = NextPrime[p^3], {6}] (* T. D. Noe, Sep 24 2008 *)

NestList[NextPrime[#^3] &, 2, 5] (* Harvey P. Dale, Feb 28 2012 *)

CROSSREFS

Cf. A001358, A055496, A076656, A006992, A005384, A005385, A118908, A118909, A118910, A118911, A118912, A118913.

Cf. A224845 (integer lengths of Mills primes).

Cf. A108739 (sequence of offsets b_n associated with Mills primes).

Cf. A051021 (decimal expansion of Mills constant).

Sequence in context: A034388 A131316 A062636 * A095820 A101295 A131306

Adjacent sequences:  A051251 A051252 A051253 * A051255 A051256 A051257

KEYWORD

nonn,nice

AUTHOR

Simon Plouffe.

EXTENSIONS

Edited by N. J. A. Sloane, May 05 2007

STATUS

approved

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Last modified December 3 18:47 EST 2016. Contains 278745 sequences.