|
|
A131043
|
|
Number of primes between 10^n and 10^n+10^(n-1).
|
|
1
|
|
|
1, 4, 16, 106, 861, 7216, 61938, 541854, 4814936, 43336106, 394050419, 3612791400, 33353349498, 309745405634, 2891246183239, 27107799609004, 255151905596682, 2409933230413924, 22832347500212719, 216919281298152512, 2066001163137387739, 19721816247905813257
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
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.
|
|
LINKS
|
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]
|
|
EXAMPLE
|
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.
|
|
PROG
|
(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), ", "))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|