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

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