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A006879 Number of primes with n digits.
(Formerly M3577)
+0
14
0, 4, 21, 143, 1061, 8363, 68906, 586081, 5096876, 45086079, 404204977, 3663002302, 33489857205, 308457624821, 2858876213963, 26639628671867, 249393770611256, 2344318816620308, 22116397130086627, 209317712988603747, 1986761935284574233, 18906449883457813088, 180340017203297174362 (list; graph; listen)
OFFSET

0,2

COMMENT

Also, the number of primes between 10^(n-1) and 10^n. - Cino Hilliard (hillcino368(AT)hotmail.com), May 31 2008 (Corrected by Jon 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. Prentice-Hall, Englewood Cliffs, NJ, 1987, p. 77.

P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, 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

C. K. Caldwell, How Many Primes Are There?

Index entries for sequences related to numbers of primes in various ranges

Cino Hilliard Count,Sum primes in a range Win32 Gcc+Gmp.

FORMULA

a(n) = pi(10^n)-pi(10^(n-1)) where pi(10^(-1)) := 0 (cf. A000720).

EXAMPLE

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

CROSSREFS

First differences of A006880.

Sequence in context: A120368 A053482 A158577 this_sequence A163861 A006153 A025164

Adjacent sequences: A006876 A006877 A006878 this_sequence A006880 A006881 A006882

KEYWORD

nonn,base,hard

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)

EXTENSIONS

11-th and 12th terms corrected by Jud McCranie (j.mccranie(AT)comcast.net) and Enoch Haga (Enokh(AT)comcast.net); 19th term corrected and 20th term added by Paul.Zimmermann(AT)loria.fr (Paul Zimmermann).

Two more terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 07 2001

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Last modified November 27 22:38 EST 2009. Contains 167602 sequences.


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