A131043 Number of primes between 10^n and 10^n+10^(n-1).

1, 4, 16, 106, 861, 7216, 61938, 541854, 4814936, 43336106, 394050419, 3612791400, 33353349498, 309745405634, 2891246183239, 27107799609004, 255151905596682, 2409933230413924, 22832347500212719, 216919281298152512, 2066001163137387739, 19721816247905813257

Offset: 1

Author

Cino Hilliard, Sep 23 2007

Keywords

• nonn

Comments

The PARI script is good up to n=9. The last 3 terms were computed by the gcc 4.1.2 program in the link. A good approximation for the n-th term is R(10^n+10^(n-1))-R(10^n) where R(x) is Riemann's approximation of the number of prime numbers < x. This is included in the PARI script. for example, Rpr11(12) = 3612792548.5108.., accurate for the first 6 digits.

Examples

			For n=2, the 4 primes in the range 100 to 110 are 101,103,107,109. So 4 is the second entry in the sequence.
		

Links

• Cino Hilliard, Count primes in a range.
• Cino Hilliard, Count primes in a range up to 10^18, message 58 in seqfun Yahoo group, providing code for gcc (needs formatting to become compilable), Sep 23, 2007. [Cached copy]

Crossrefs

Cf. A006880, A309329.

Programs

PARI

/*Some functions*/ pr11(n) = primepi(10^n+10^(n-1))-primepi(10^n) Rpr11(n) = R(10^n+10^(n-1))-R(10^(n)) R(x) = local(j); (sum(j=1,400,moebius(j)*Li(x^(1/j))/j)) /*End functions*/ for(x=1,9,print1(pr11(x),","))

Extensions

a(13)-a(19) from Hugo Pfoertner, Nov 16 2019

a(20)-a(21) from Chai Wah Wu, Nov 29 2019

a(22) from Chai Wah Wu, Nov 30 2019