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 A370850 #22 Mar 25 2024 21:58:14
%S A370850 2,3,5,13,11113,111111113,11111111111111111111111111117
%N A370850 Lesser of two consecutive primes whose digits' products are also prime.
%C A370850 If it exists, a(8) > 10^500. - _Hugo Pfoertner_, Mar 03 2024
%C A370850 If it exists, a(8) > 10^10000. - _Bert Dobbelaere_, Mar 16 2024
%e A370850 13 is a term because 13 is prime, the product of its digits is 3 which is prime and the product of the digits of 17, the next prime to 13, is 7 and 7 is prime.
%e A370850 19 is not a term because the product of its digits is 9 and 9 is not prime.
%e A370850 131 is not a term because although it is prime and the product of its digits is 3 which is also prime, the product of the digits of 137, the next prime to 131, is 21 and 21 is not prime.
%t A370850 Select[Prime[Range[10^5]], PrimeQ[Apply[Times, IntegerDigits[#]]]&&PrimeQ[Apply[Times, IntegerDigits[NextPrime[#]]]]&] (* _James C. McMahon_, Mar 03 2024 *)
%o A370850 (PARI) isok(p)=my(x=vecprod(digits(p)),y=vecprod(digits(nextprime(p+1))));isprime(x) && isprime(y);
%o A370850 forprime(p=2,20000,if(isok(p),print1(p", ")))
%o A370850 (PARI) a370850(maxdigits=100) = {my(L=List()); for (n=1, maxdigits, my (r=(10^n-1)/9, d=digits(r)); foreach ([2,3,5,7], s, for (k=1, #d, my(dd=d); dd[k]=s; my (q=fromdigits(dd)); if (ispseudoprime(q) && isprime(vecprod(digits(nextprime(q+1)))), listput(L,q))))); vecsort(Vec(L))};
%o A370850 a370850() \\ _Hugo Pfoertner_, Mar 03 2024
%Y A370850 Cf. A000040, A053666.
%Y A370850 Cf. also A370848, A370851.
%K A370850 nonn,base,hard
%O A370850 1,1
%A A370850 _Claude H. R. Dequatre_, Mar 03 2024
%E A370850 a(7) from _Hugo Pfoertner_, Mar 03 2024