A038822 Number of primes between 100n and 100n+99.

25, 21, 16, 16, 17, 14, 16, 14, 15, 14, 16, 12, 15, 11, 17, 12, 15, 12, 12, 13, 14, 10, 15, 15, 10, 11, 15, 14, 12, 11, 12, 10, 11, 15, 11, 14, 13, 12, 11, 11, 15, 9, 16, 9, 11, 12, 12, 12, 8, 15, 12, 11, 10, 10, 13, 13, 12, 10, 16, 7, 12, 11, 13, 15, 8, 11, 10, 12, 12, 13, 9, 10

Offset: 0

Author

Jeff Burch

Keywords

• nonn

Comments

The number k first occurs in century A186311(k).

Examples

			a(3) = 16 because there are 16 primes between 300 and 399 (namely, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397).
a(4) = 17 because there are 17 primes between 400 and 499 (401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499).
		

References

• George P. Loweke, The Lore of Prime Numbers. New York: Vantage Press (1982): 91.

Links

• T. D. Noe, Table of n, a(n) for n = 0..9999

Crossrefs

Cf. A028505.

Cf. A181098 (centuries without primes).

Cf. A186393-A186408 (centuries having 1 to 16 primes), A186509 (17 primes).

Cf. A094892, A098592.

Programs

Maple

with(numtheory); A038822 := n->pi(100*n+99)-pi(100*n); seq(A038822(k), k=0..100); # Wesley Ivan Hurt, Oct 03 2013

Mathematica

Table[PrimePi[100n + 99] - PrimePi[100n], {n, 0, 71}]
Differences[PrimePi[100 Range[0,100]]] (* Harvey P. Dale, Feb 18 2021 *)

PARI

a(n)=sum(i=100*n,100*n+99,isprime(i)) \\ Charles R Greathouse IV, Apr 28 2015

PARI

a(n)= my(r=0, p=100*n, q=p+99); while((p=nextprime(p+1))<=q, r+=isprime(p)); r; \\ Ruud H.G. van Tol, Nov 17 2024

Formula

a(n) = pi(100n+99) - pi(100n). - Wesley Ivan Hurt, Oct 03 2013

Extensions

Edited, corrected and extended by Robert G. Wilson v, Jan 29 2003