Prime containment numbers (golf edition)
05AB1E, 8 bytes

∞.ΔIÅpåP


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Explanation

           # from
∞          # a list of infinite positive integers
 .Δ        # find the first which satisfies the condition:
       P   # all
   IÅp     # of the first &lt;input&gt; prime numbers
      å    # are contained in the number