A006879 Number of primes with n digits. (Formerly M3577)

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

Offset

0,2

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]

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

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

Formula

a(n) = pi(10^n)-pi(10^(n-1)) 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.

Mathematica

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

Prog

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

Crossrefs

First differences of A006880.

Cf. A309329.

Sequence in context: A120368 A053482 A158577 * A228063 A228111 A305986

Adjacent sequences: A006876 A006877 A006878 * A006880 A006881 A006882

Keyword

nonn,base,hard,changed

Author

N. J. A. Sloane, Simon Plouffe

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

Status

approved