A370851 - OEIS

A370851

Lesser of two consecutive primes such that the product of its digits is also prime and that of the other is composite.

17, 31, 71, 113, 131, 151, 211, 311, 1117, 1151, 1171, 1511, 2111, 11117, 11131, 11171, 11311, 111121, 111211, 112111, 113111, 131111, 311111, 511111, 1111151, 1111211, 1111711, 1117111, 1171111, 11111117, 11111131, 11111171, 11111311, 11113111, 11131111, 71111111

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..36.

EXAMPLE

17 is a term because 17 is prime, the product of its digits is 7 which is prime and the product of the digits of 19, the next prime to 17, is 9 and 9 is composite.

13 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 17, the next prime to 13, is 7 and 7 is not composite.

29 is not a term because the product of its digits is 18 and 18 is not prime.

MATHEMATICA

Select[Prime[Range[6*10^6]], PrimeQ[Apply[Times, IntegerDigits[#]]]&&CompositeQ[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) && y>3 &&!isprime(y);

forprime(p=2, 20000, if(isok(p), print1(p", ")))

(Python)

from math import prod

from itertools import count, islice

from sympy import isprime, nextprime

def A370851_gen(): # generator of terms

for l in count(1):

k = (10**l-1)//9

for m in range(l):

a = 10**m