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Products of 5 distinct primes a,b,c,d,e, such that a+b+c+d+e are prime numbers.
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%I #6 May 26 2024 01:10:23

%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.

%e 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