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%I #3 Mar 31 2012 10:29:09
%S 1,11,30,63,116,187,281
%N Maximal number of distinct primes in the solution of the n X n generalization of the Gordon Lee puzzle.
%C The Gordon Lee puzzle asks for an n X n array of single digits such that as many distinct primes as possible are formed by joining consecutive digits in any horizontal, vertical or diagonal direction, forward or backward. a(4)=63 was proved in March 2005 by Mike Oakes. a(5) and a(6) are conjectured best values that resisted any improvement since 1998.
%C a(5), a(6) and a(7) are conjectured best values that have resisted any improvement since 1998, including the joint effort of more than 100 participants in a programming contest in summer 2005. The best currently (September 2005) known lower bounds for the next terms are a(8)>=394 and a(9)>=527. - _Hugo Pfoertner_, Sep 21 2005
%H Carlos Rivera, <a href="http://www.recmath.org/contest/PrimeSquares/index.php">The Gordon Lee puzzle.</a>
%H Carlos Rivera, <a href="http://www.recmath.org/contest/PrimeSquares/BestSolutions1.php">Best Solutions</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeArray.html">Prime Array.</a>
%H Al Zimmermann's Programming Contests. Primal Squares: <a href="http://www.recmath.org/contest/BestSolutions1.php">Best grids for part 1 found during the contest.</a>
%Y Cf. A032529 = all primes in the 3 X 3 record matrix, A034720 = number of candidates to be checked for primality in an n X n matrix of single digits.
%Y A111128 gives the solutions to Part 2 of the contest.
%K hard,more,nonn
%O 1,2
%A _Hugo Pfoertner_, Jul 05 2005
%E a(7) from _Hugo Pfoertner_, Sep 21 2005
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