A046703 Multiplicative primes: product of digits is a prime.

2, 3, 5, 7, 13, 17, 31, 71, 113, 131, 151, 211, 311, 1117, 1151, 1171, 1511, 2111, 11113, 11117, 11131, 11171, 11311, 111121, 111211, 112111, 113111, 131111, 311111, 511111, 1111151, 1111211, 1111711, 1117111, 1171111, 11111117, 11111131, 11111171, 11111311, 11113111, 11131111

Offset: 1

Author

Felice Russo

Keywords

• base
• nonn

Comments

Primes with one prime digit and all other digits are 1. The linked table includes probable primes. - Jens Kruse Andersen, Jul 21 2014

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A117835 ("noncomposite" variant), A007954 (product of digits), A028842 (product of digits is prime).

Programs

Mathematica

Select[Prime[Range[740000]],PrimeQ[Times@@IntegerDigits[#]]&] (* Harvey P. Dale, Oct 02 2011 *)
Select[FromDigits/@Flatten[Table[Permutations[PadRight[{p},n,1]],{n,8},{p,{2,3,5,7}}],2],PrimeQ]//Union (* Harvey P. Dale, Nov 21 2019 *)

PARI

f(n,b,d) = if(d, f(10*n+1, b, d-1); if(!b, forprime(q=2, 9, f(10*n+q, 1, d-1))), if(b && isprime(n), print1(n", ")))
for(d=1, 8, f(0,0,d)) \\ f(0,0,d) prints d-digit terms. Jens Kruse Andersen, Jul 21 2014

PARI

\\ From M. F. Hasler, Apr 23 2019: (Start)
select( is_A046703(n)=isprime(vecprod(digits(n)))&&ispseudoprime(n), [0..9999]) \\ This defines is_A046703(). In older PARI versions, vecprod=factorback.
next_A046703(n)={if( n>1, until( ispseudoprime(n), my(d=digits(n)); n=fromdigits( apply( t->if(t>1, nextprime(t+1), 1), d))+(d[1]>5)); n, 2)}
A046703_vec(N=99)=vector(N, i, t=next_A046703(if(i>1, t))) \\ (End)

Extensions

Corrected by Harvey P. Dale, Oct 02 2011