1,2

Numbers n such that there is no pair of twin primes P, P+2 with n^2 < P < P+2 < n^2+2*n.

The first 7 terms of this sequence were given by Ernst Jung in a discussion in the Newsgroup de.sci.mathematik entitled "Primzahlen zwischen (2x-1)^2 und (2x+1)^2" (primes between ...and...) with other significant contributions from Hermann Kremer and Rainer Rosenthal. It is conjectured that there are no further terms beyond a(11)=122. This has been tested to 50000 by Robert G. Wilson v (rgwv(AT)rgwv.com).

Hugo Pfoertner, Illustration of record gaps between pairs of twin primes.

Eric Weisstein's World of Mathematics, k-Tuple Conjecture Section in World of Mathematics.

Eric Weisstein's World of Mathematics, Twin Prime Conjecture Section in World of Mathematics.

a(1)=9 because no twin primes are found in the interval [9^2,10^2].

isA091592 := proc(n) local p; p := nextprime(n^2) ; q := nextprime(p) ; while q < n^2+2*n do if q-p = 2 then RETURN(false) ; fi; p :=q ; q := nextprime(p) ; od: RETURN(true) ; end: for n from 1 do if isA091592(n) then printf("%d ", n) ; fi; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 26 2008]

fQ[n_] := StringCount[ ToString@ PrimeQ[ Range[n^2, (n + 1)^2]], "True, False, True"] == 0; lst = {}; Do[ If[ fQ@n, AppendTo[lst, n]], {n, 25000}]

Cf. A091591, A036061, A036063.

Sequence in context: A079368 A167529 A106677 this_sequence A145906 A090065 A098791

Adjacent sequences: A091589 A091590 A091591 this_sequence A091593 A091594 A091595

hard,nonn

Hugo Pfoertner (hugo(AT)pfoertner.org), Jan 25 2004

Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 31 2008 at the suggestion of Pierre CAMI