A006879 Number of primes with n digits.

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

Offset: 0

Author

N. J. A. Sloane, Simon Plouffe

Keywords

• nonn
• base
• hard

Comments

The number of primes between 10^(n-1) and 10^n. - Cino Hilliard, May 31 2008 [Corrected by Jon E. Schoenfield, Nov 29 2008]

Examples

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

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).
• James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 113.

Links

• Jianing Song, Table of n, a(n) for n = 0..29 (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)
• C. K. Caldwell, How Many Primes Are There?
• Vladimir Pletser, Global Generalized Mersenne Numbers: Definition, Decomposition, and Generalized Theorems, Preprints.org, 2024. See p. 20.
• Index entries for sequences related to numbers of primes in various ranges

Crossrefs

First differences of A006880.

Cf. A309329.

Programs

Mathematica

Differences[PrimePi[10^Range[-1, 25]]] (* Paolo Xausa, Apr 16 2024 *)

PARI

a(n)=primepi(10^n)-primepi(10^(n-1)) \\ Charles R Greathouse IV, May 03 2012

Formula

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

Extensions

a(11) and a(12) corrected by Jud McCranie and Enoch Haga

a(19) corrected and a(20) added by Paul Zimmermann

a(21)-a(22) from Vladeta Jovovic, Nov 07 2001