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%I #14 May 07 2021 09:30:53
%S 7,37,457,8647,51315414607
%N Primes which are two greater than A097492 terms.
%C The next term (17866..79237) has 186 digits.
%e a(4) = 8647 = (Product_{k=1..4} A006512(k)) + 2 = 5*7*13*19 + 2 = A097492(4) + 2. - _Hartmut F. W. Hoft_, Apr 27 2021
%t step[{list_, q_}] := Module[{p=NextPrime[q]}, {Join[list, If[PrimeQ[p+2], {{p,p+2}}, {}]], p}]
%t largerTwin[n_] := Last[Transpose[First[NestWhile[step, {{{3, 5}}, 3}, Length[First[step[#]]]<=n&]]]]
%t a097492[n_] := Rest[FoldList[Times, 1, largerTwin[n]]]
%t a097493[n_] := Select[Map[#+2&, a097492[n]], PrimeQ]
%t a097493[68] (* _Hartmut F. W. Hoft_, Apr 27 2021 *)
%o (PARI) fu(n) = p=1;for(x=1,n,p*=twinu(x);if(isprime(p+2),print1(p+2","))) \The n-th upper twin prime twinu(n) = { local(c,x); c=0; x=1; while(c<n, if(isprime(prime(x)+2),c++); x++; ); return(prime(x)) }
%Y Cf. A097490, A097491, A097492.
%Y Cf. A001359, A077800, A097489.
%K nonn
%O 1,1
%A _Cino Hilliard_, Aug 24 2004
%E Edited by _Don Reble_, Apr 16 2007
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