# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a091592 Showing 1-1 of 1 %I A091592 #32 Oct 23 2023 10:45:03 %S A091592 1,9,19,26,27,30,34,39,49,53,77,122 %N A091592 Numbers n such that there are no twin primes between n^2 and (n+1)^2. %C A091592 Numbers n such that there is no pair of twin primes P, P+2 with n^2 < P < P+2 < n^2+2*n. %C A091592 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(12)=122. This has been tested to 50000 by _Robert G. Wilson v_. %C A091592 Tested up to 10^7 and found no such numbers. - _Arkadiusz Wesolowski_, Jul 11 2011 %H A091592 J. Korevaar, The prime-pair conjectures of Hardy and Littlewood, Indagationes Mathematicae, Volume 23, Issue 3, 2012, Pages 269-299. %H A091592 A. Kourbatov, Maximal Gaps Between Prime k-Tuples: A Statistical Approach, J. Int. Seq. 16 (2013) #13.5.2 %H A091592 Hugo Pfoertner, Illustration of record gaps between pairs of twin primes. %H A091592 Eric Weisstein's World of Mathematics, k-Tuple Conjecture. %H A091592 Eric Weisstein's World of Mathematics, Twin Prime Conjecture. %e A091592 9 is a term because no twin primes are found in the interval [9^2,10^2]. %p A091592 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: # _R. J. Mathar_, Aug 26 2008 %t A091592 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}] %Y A091592 Cf. A091591, A036061, A036063, A113274. %K A091592 nonn,hard,more %O A091592 1,2 %A A091592 _Hugo Pfoertner_, Jan 25 2004 %E A091592 Edited by _N. J. A. Sloane_, Aug 31 2008 at the suggestion of _Pierre CAMI_ # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE