A370850 Lesser of two consecutive primes whose digits' products are also prime.

2, 3, 5, 13, 11113, 111111113, 11111111111111111111111111117

Offset

1,1

Comments

If it exists, a(8) > 10^500. - Hugo Pfoertner, Mar 03 2024

If it exists, a(8) > 10^10000. - Bert Dobbelaere, Mar 16 2024

Links

Table of n, a(n) for n=1..7.

Example

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.
19 is not a term because the product of its digits is 9 and 9 is not prime.
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.

Mathematica

Select[Prime[Range[10^5]], PrimeQ[Apply[Times, IntegerDigits[#]]]&&PrimeQ[Apply[Times, IntegerDigits[NextPrime[#]]]]&] (* James C. McMahon, Mar 03 2024 *)

Prog

(PARI) isok(p)=my(x=vecprod(digits(p)), y=vecprod(digits(nextprime(p+1)))); isprime(x) && isprime(y);
forprime(p=2, 20000, if(isok(p), print1(p", ")))
(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))};
a370850() \\ Hugo Pfoertner, Mar 03 2024

Crossrefs

Cf. A000040, A053666.

Cf. also A370848, A370851.

Sequence in context: A042907 A115347 A173654 * A126333 A266192 A233082

Adjacent sequences: A370847 A370848 A370849 * A370851 A370852 A370853

Keyword

nonn,base,hard

Author

Claude H. R. Dequatre, Mar 03 2024

Extensions

a(7) from Hugo Pfoertner, Mar 03 2024

Status

approved