OFFSET
1,2
COMMENTS
From Bertrand's postulate (i.e., there is always a prime p in the range n < p < 2n) one can show there is a constant b such that floor(2^b), floor(2^2^b), ..., floor(2^2^2...^b), ... are all primes.
This result is due to Wright (1951), so Bertrand's constant might be better called Wright's constant, by analogy with Mills's constant A051021. - Jonathan Sondow, Aug 02 2013
REFERENCES
S. Finch, Mathematical Constants, Cambridge Univ. Press, 2003; see section 2.13 Mills's constant.
LINKS
C. K. Caldwell, Prime Curios! 137438953481.
Pierre Dusart, Estimates of some functions over primes without R. H., arXiv:1002.0442 [math.NT], 2010.
J. Sondow, E. Weisstein, Bertrand's Postulate.
E. M. Wright, A prime-representing function, Amer. Math. Monthly, 58 (1951), 616-618.
FORMULA
1.251647597790463017594432053623346969...
EXAMPLE
2^(2^(2^1.251647597790463017594432053623)) is approximately 37.0000000000944728917062132870071 and A051501(3)=37.
CROSSREFS
KEYWORD
AUTHOR
Benoit Cloitre, Jan 29 2003
EXTENSIONS
More digits (from the Prime Curios page) added by Frank Ellermann, Sep 19 2011
a(16)-a(37) from Charles R Greathouse IV, Sep 20 2011
Definition clarified by Jonathan Sondow, Aug 02 2013
STATUS
approved