login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A093683 Number of pairs of twin primes <= 10^n-th prime. 2
4, 25, 174, 1270, 10250, 86027, 738597, 6497407, 58047180, 524733511 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence is >= the values of pi(10^n): 4, 25, 168, 1229, . . . in A006880.

REFERENCES

Enoch Haga, "Wandering through a prime number desert," Table 6, in Exploring prime numbers on your PC and the Internet, 2001 (ISBN 1-885794-17-7).

LINKS

Table of n, a(n) for n=1..10.

Soren Laing Aletheia-Zomlefer, Lenny Fukshansky, and Stephan Ramon Garcia, The Bateman-Horn Conjecture: Heuristics, History, and Applications, arXiv:1807.08899 [math.NT], 2018-2019. See Table 5 p. 40.

Thomas R. Nicely, Twin prime count.

Index entries for sequences related to numbers of primes in various ranges

FORMULA

Count twin primes <= p_{10^n}: 10th prime, 100th prime, etc.

EXAMPLE

a(1) = 4 because there are 4 twin primes <= 29, the 10th prime: (3,5), (5,7), (11,13), and (17,19). (29,31) is not counted because it is not entirely <= 29.

MATHEMATICA

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; c = 0; p = q = 1; Do[l = Prime[10^n]; While[q <= l, If[p + 2 == q, c++ ]; p = q; q = NextPrim[p]]; Print[c], {n, 12}] (* Robert G. Wilson v, Apr 10 2004 *)

PROG

(Python)

from sympy import prime, sieve # use primerange for larger terms

def afind(terms):

  c, prevp = 0, 1

  for n in range(1, terms+1):

    for p in sieve.primerange(prevp+1, prime(10**n)+1):

      if prevp == p - 2: c += 1

      prevp = p

    print(c, end=", ")

afind(6) # Michael S. Branicky, Apr 25 2021

CROSSREFS

See A049035 for another version. - R. J. Mathar, Sep 05 2008

Cf. A006880, A007508, A049035.

Sequence in context: A140177 A034494 A084210 * A006348 A213608 A324169

Adjacent sequences:  A093680 A093681 A093682 * A093684 A093685 A093686

KEYWORD

nonn,more

AUTHOR

Enoch Haga, Apr 09 2004

EXTENSIONS

a(9) from Michael S. Branicky, Apr 25 2021

a(10) from Eduard Roure Perdices, May 08 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 20 23:39 EDT 2021. Contains 345314 sequences. (Running on oeis4.)