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%I #35 Jan 26 2023 11:18:36
%S 3,6,2,4,6,1,5,3,1,2,4,3,1,3,2,1,3,2,3,3,1,0,1,0,1,6,1,2,0,4,0,2,2,1,
%T 2,2,0,3,0,1,0,4,4,1,0,1,2,0,3,1,1,1,0,1,1,0,3,4,1,0,1,4,1,2,0,1,1,2,
%U 1,1,1,1,2,1,2,2,0,2,0,1,1,1,2,1,0,1,3
%N a(n) = floor(10*(prime(n+1)-prime(n))/log(prime(n))^2).
%C Cramer's conjecture is true if, for every n >= 5, a(n) is smaller than 10.
%C If Cramer's conjecture is true, then Andrica's conjecture is true. [_John W. Nicholson_, Feb 06 2012]
%C Some mathematicians are trying to prove: if Andrica's conjecture is true, then Cramer's conjecture is true. [_Arkadiusz Wesolowski_, Feb 22 2012]
%H Arkadiusz Wesolowski, <a href="/A200474/b200474.txt">Table of n, a(n) for n = 5..10000</a>
%H Carlos Rivera, <a href="http://www.primepuzzles.net/conjectures/conj_007.htm">Conjecture 7. The Cramer's Conjecture</a>, The Prime Puzzles and Problems Connection.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CramerConjecture.html">Cramer Conjecture</a>
%F a(n) = floor(10*A001223(n)/log(A000040(n))^2), n >= 5.
%e a(9) = 6 because 10*(29-23)/log(23)^2 = 6.1029419977....
%t Table[Floor[10*(Prime[n + 1] - Prime[n])/Log[Prime[n]]^2], {n, 5, 100}]
%Y Cf. A000040, A001223, A086142, A124129, A200324.
%K nonn
%O 5,1
%A _Arkadiusz Wesolowski_, Nov 18 2011
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