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Primes p with no zero digits such that (the digit product of p) plus p is also prime.
5

%I #16 May 20 2021 04:45:04

%S 23,29,61,67,83,163,233,239,283,293,347,349,431,439,443,449,499,563,

%T 569,613,617,619,653,659,677,683,743,929,941,1123,1163,1217,1231,1237,

%U 1249,1289,1297,1321

%N Primes p with no zero digits such that (the digit product of p) plus p is also prime.

%H Charles R Greathouse IV, <a href="/A092518/b092518.txt">Table of n, a(n) for n = 1..10000</a>

%e a(2) = 29: 29+2(9) = 29+18 = 47 which is prime.

%t Select[Prime[Range[300]],DigitCount[#,10,0]==0&&PrimeQ[#+Times@@ IntegerDigits[ #]]&] (* _Harvey P. Dale_, Jan 27 2020 *)

%o (PARI) dprod(n)=n=digits(n); prod(i=1, #n, n[i])

%o is(n)=my(d=dprod(n)); d && isprime(n+d) && isprime(n) \\ _Charles R Greathouse IV_, Dec 27 2013

%Y Cf. A053666.

%K nonn,base

%O 1,1

%A _Ray G. Opao_, Apr 06 2004

%E Definition clarified by _Harvey P. Dale_, Jan 27 2020