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%I #4 Aug 07 2013 14:44:01
%S 19635,25935,42315,47355,51765,54285,57057,58695,61215,62205,64515,
%T 70035,72105,73185,73815,76245,82005,83265,83895,85085,86955,87945,
%U 88179,90321,90915,95865,96135,99015,99645,100815,103785,107835,110055
%N Products of 5 distinct primes a,b,c,d,e, such that a+b+c+d+e are prime numbers.
%C 19635=3*5*7*11*17,3+5+7+11+17=43,..
%t f[n_]:=Last/@FactorInteger[n]=={1,1,1,1,1}&&PrimeQ[Plus@@First/@FactorInteger[n]];lst={};Do[If[f[n],AppendTo[lst,n]],{n,9!}];lst
%t With[{nn=40},Take[Union[Times@@#&/@Select[Subsets[Prime[Range[nn]],{5}], PrimeQ[Total[#]]&]],nn]] (* _Harvey P. Dale_, Aug 07 2013 *)
%Y Cf. A176877
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jun 12 2010
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