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%I #3 Oct 01 2013 21:35:21
%S 5,7,11,13,17,19,23,37,29,31,47,37,41,43,47,61,53,67,59,61,227,67,71,
%T 73,89,79,83,97,89,103,107,97,101,103
%N First prime which is 2k greater than the product of lesser twin primes.
%C In the example, 37 is the only number possible for 2k=22. Twinl#(1)= 3 and 3+22 = 25, not prime. Twinl#(n), n>2, is a multiple of 11 so adding 22 will always result in a multiple of 11 and not prime. If k is a multiple of a lesser twin prime, then the number of primes in twinl#(n)+2k is finite.
%F Define twinl#(n)as the product of the first n lesser twin primes. Then if twinl#+2k k=1,2,3... is prime, list it.
%e Twinl#(2) + 2*11 = 37, the first prime 22 greater than twinl#(2).
%o (PARI) twiprimesl(n,a) = { local(pr,x,y,j); for(j=1,n, pr=1; for(x=1,j, pr*=twinl(x); ); y=pr+a; if(ispseudoprime(y), print1(y",") ) ) } twinl(n) = \The n-th lower twin prime { local(c,x); c=0; x=1; while(c<n, if(isprime(prime(x)+2),c++); x++; ); return(prime(x-1)) }
%K nonn
%O 1,1
%A _Cino Hilliard_, May 08 2007
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