

A006879


Number of primes with n digits.
(Formerly M3577)


43



0, 4, 21, 143, 1061, 8363, 68906, 586081, 5096876, 45086079, 404204977, 3663002302, 33489857205, 308457624821, 2858876213963, 26639628671867, 249393770611256, 2344318816620308, 22116397130086627, 209317712988603747, 1986761935284574233, 18906449883457813088, 180340017203297174362
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OFFSET

0,2


COMMENTS

The number of primes between 10^(n1) and 10^n.  Cino Hilliard, May 31 2008 (Corrected by Jon E. Schoenfield, Nov 29 2008)


REFERENCES

J.M. De Koninck, Ces nombres qui nous fascinent, Entry 21, pp 8, Ellipses, Paris 2008.
C. T. Long, Elementary Introduction to Number Theory. PrenticeHall, Englewood Cliffs, NJ, 1987, p. 77.
P. Ribenboim, The Book of Prime Number Records. SpringerVerlag, NY, 2nd ed., 1989, p. 179.
D. Shanks, Solved and Unsolved Problems in Number Theory. Chelsea, NY, 2nd edition, 1978, p. 15.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Vladimir Pletser, Table of n, a(n) for n = 0..25 (terms 0..24 by Charles R Greathouse IV).
C. K. Caldwell, How Many Primes Are There?
G. T. Leavens and M. Vermeulen, 3x+1 search programs, Computers and Mathematics with Applications, 24 (1992), 7999. (Annotated scanned copy)
Index entries for sequences related to numbers of primes in various ranges


FORMULA

a(n) = pi(10^n)pi(10^(n1)) where pi(10^(1)) := 0 (cf. A000720 and A006880).


EXAMPLE

As 2, 3, 5, and 7 are the only primes less than 10, a(1) = 4.


PROG

(PARI) a(n)=primepi(10^n)primepi(10^(n1)) \\ Charles R Greathouse IV, May 03 2012


CROSSREFS

First differences of A006880.
Sequence in context: A120368 A053482 A158577 * A228063 A228111 A305986
Adjacent sequences: A006876 A006877 A006878 * A006880 A006881 A006882


KEYWORD

nonn,base,hard


AUTHOR

N. J. A. Sloane, Simon Plouffe


EXTENSIONS

11th and 12th terms corrected by Jud McCranie and Enoch Haga; 19th term corrected and 20th term added by Paul Zimmermann.
a(21)a(22) from Vladeta Jovovic, Nov 07 2001


STATUS

approved



