This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A225863 #10 Nov 20 2020 17:06:14
%S A225863 19,37,53,59,73,79,97,103,107,109,127,149,163,167,181,233,239,251,257,
%T A225863 271,277,293,307,347,349,367,383,389,419,431,433,439,457,479,491,499,
%U A225863 503,509,521,523,541,547,563,569,587,613,617,619,631,653,659,673
%N A225863 Primes for which both sum and product of digits are nonprimes.
%e A225863 79 is a member since neither 7 + 9 = 16 nor 7 * 9 = 63 is prime.
%t A225863 d[n_]:=IntegerDigits[n]; Select[Prime[Range[122]],!PrimeQ[Plus@@(x=d[#])] && !PrimeQ[Times@@x] &]
%t A225863 Select[Prime[Range[150]],NoneTrue[{Total[IntegerDigits[#]],Times@@ IntegerDigits[ #]},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Nov 20 2020 *)
%Y A225863 Cf. A046713.
%K A225863 nonn,base
%O A225863 1,1
%A A225863 _Jayanta Basu_, May 18 2013