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A112229 Table of the smallest (x,y) pairs such that x*n+1 is prime, y*n+1 is a larger prime, and (x*n+1)*(y*n+1)-2 is also prime. 1

%I

%S 2,4,1,2,2,4,1,4,2,8,1,2,4,28,2,11,2,4,1,4,2,32,1,3,4,40,2,14,2,4,1,

%T 37,6,138,1,2,10,40,2,5,2,16,1,16,2,26,3,4,4,10,2,20,4,10,1,7,2,50,1,

%U 2,10,22,3,6,2,6,3,69,2,8,1,2,4,40,5,20,2,4,1,7,2,20,1,8,4,10,2,32,4,12,1,13

%N Table of the smallest (x,y) pairs such that x*n+1 is prime, y*n+1 is a larger prime, and (x*n+1)*(y*n+1)-2 is also prime.

%C The associated (x*n+1)*(y*n+1) for a solution is a semiprime, so the (x*n+1)*(y*n+1)-2 are actually Chen primes.

%C If more than one pair exists for a given n, priority is given to minimize x, the smaller prime.

%e For n=3, (x,y)=(2,4), 2*3+1=7 is prime, 4*3+1=13 is prime, and 7*13-2=89 is a Chen prime.

%e 2,4;

%e 1,2;

%e 2,4;

%e 1,4;

%e 2,8;

%e 1,2;

%e 4,28;

%e 2,11;

%e 2,4;

%e 1,4;

%e 2,32;

%e 1,3;

%e 4,40;...

%Y Cf. A112230.

%K nonn,tabf

%O 1,1

%A _Pierre CAMI_, Aug 29 2005

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