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A006879 Number of primes with n digits.

%I A006879 M3577 #87 Jul 15 2025 11:36:02
%S A006879 0,4,21,143,1061,8363,68906,586081,5096876,45086079,404204977,
%T A006879 3663002302,33489857205,308457624821,2858876213963,26639628671867,
%U A006879 249393770611256,2344318816620308,22116397130086627,209317712988603747,1986761935284574233,18906449883457813088,180340017203297174362
%N A006879 Number of primes with n digits.
%C A006879 The number of primes between 10^(n-1) and 10^n. - _Cino Hilliard_, May 31 2008 [Corrected by _Jon E. Schoenfield_, Nov 29 2008]
%D A006879 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 21, pp 8, Ellipses, Paris 2008.
%D A006879 C. T. Long, Elementary Introduction to Number Theory. Prentice-Hall, Englewood Cliffs, NJ, 1987, p. 77.
%D A006879 P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 179.
%D A006879 D. Shanks, Solved and Unsolved Problems in Number Theory. Chelsea, NY, 2nd edition, 1978, p. 15.
%D A006879 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A006879 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 113.
%H A006879 Jianing Song, <a href="/A006879/b006879.txt">Table of n, a(n) for n = 0..29</a> (terms 0..24 by Charles R Greathouse IV, a(25) by Vladimir Pletser, a(26)-a(28) from David Baugh, a(29) based on A006880)
%H A006879 C. K. Caldwell, <a href="http://www.utm.edu/research/primes/howmany.shtml">How Many Primes Are There?</a>
%H A006879 Vladimir Pletser, <a href="https://doi.org/10.20944/preprints202402.0545.v1">Global Generalized Mersenne Numbers: Definition, Decomposition, and Generalized Theorems</a>, Preprints.org, 2024. See p. 20.
%H A006879 <a href="/index/Pri#primepop">Index entries for sequences related to numbers of primes in various ranges</a>
%F A006879 a(n) = pi(10^n)-pi(10^(n-1)) where pi(10^(-1)) := 0 (cf. A000720 and A006880).
%e A006879 As 2, 3, 5, and 7 are the only primes less than 10, a(1) = 4.
%t A006879 Differences[PrimePi[10^Range[-1, 25]]] (* _Paolo Xausa_, Apr 16 2024 *)
%o A006879 (PARI) a(n)=primepi(10^n)-primepi(10^(n-1)) \\ _Charles R Greathouse IV_, May 03 2012
%Y A006879 First differences of A006880.
%Y A006879 Cf. A309329.
%K A006879 nonn,base,hard
%O A006879 0,2
%A A006879 _N. J. A. Sloane_, _Simon Plouffe_
%E A006879 a(11) and a(12) corrected by _Jud McCranie_ and _Enoch Haga_
%E A006879 a(19) corrected and a(20) added by _Paul Zimmermann_
%E A006879 a(21)-a(22) from _Vladeta Jovovic_, Nov 07 2001