Search: id:A111943
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%I A111943
%S A111943 13,23,113,1327,31397,370261,2010733,20831323,25056082087,
%T A111943 2614941710599,19581334192423,218209405436543,1693182318746371
%N A111943 Prime p with prime gap q-p of n_th record Cramer-Shanks-Granville ratio, 
               where q is smallest prime larger than p and C-S-G ratio is (q-p)/
               (log(p))^2.
%C A111943 Primes less than 23 are anomalous and are excluded.
%C A111943 The sequence ends with Bertil Nyman's 1999 discovery.
%C A111943 Shanks conjecture is that the ratio will never reach 1.
%D A111943 R. K. Guy, Unsolved Problems in Theory of Numbers, Springer-Verlag, Third 
               Edition, 2004, A8.
%H A111943 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PrimeGaps.html">Prime Gaps</a>.
%H A111943 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Cramer-GranvilleConjecture.html">Cramer-Granville Conjecture</a>.
%H A111943 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               ShanksConjecture.html">Shanks Conjecture</a> (and Wolf Conjecture.)
%e A111943 n Ratio prime:
%e A111943 2 0.6103 23
%e A111943 3 0.6264 113
%e A111943 4 0.6575 1327
%e A111943 5 0.6715 31397
%e A111943 6 0.6812 370261
%e A111943 7 0.7025 2010733
%e A111943 8 0.7394 20831323
%e A111943 9 0.7953 25056082087
%e A111943 10 0.7975 2614941710599
%e A111943 11 0.8177 19581334192423
%e A111943 12 0.8311 218209405436543
%e A111943 13 0.9206 1693182318746371
%Y A111943 Cf. A111870.
%Y A111943 Cf. A166363.
%Y A111943 Adjacent sequences: A111940 A111941 A111942 this_sequence A111944 A111945 
               A111946
%K A111943 nonn,hard,new
%O A111943 1,1
%A A111943 N. J. A. Sloane (njas(AT)research.att.com), following emails from R. 
               K. Guy and Ed Pegg, Jr., Nov 27 2005
%E A111943 Corrected and edited (p_n could be misinterpreted as the n_th prime) 
               by Daniel Forgues (squid(AT)zensearch.com), Nov 20 2009

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