Find the composite numbers k in base 10, that have no single digit prime factors and whose prime factors are all a substring of k.



Task
 Find and show here, on this page, the first ten elements of the sequence.


Stretch
 Find and show the next ten elements.




ClearAll[CompositeAndContainsPrimeFactor]
CompositeAndContainsPrimeFactor[k_Integer] := Module[{id, pf},
  If[CompositeQ[k],
   pf = FactorInteger[k][[All, 1]];
   If[AllTrue[pf, GreaterThan[10]],
    id = IntegerDigits[k];
    AllTrue[pf, SequenceCount[id, IntegerDigits[#]] > 0 &]
    ,
    False
    ]
   ,
   False
   ]
  ]
out = Select[Range[30000000], CompositeAndContainsPrimeFactor]