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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.

Chris K. Caldwell and Yuanyou Cheng, Determining Mills' Constant and a Note on Honaker's Problem, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.1.

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

LINKS

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

C. K. Caldwell, Mills' Theorem - a generalization

C. 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

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 November 25 23:44 EST 2014. Contains 250017 sequences.