A134873 Primes p with the property that the sum of the digits of the product of the digits of p is also a prime number.

2, 3, 5, 7, 13, 17, 31, 37, 43, 71, 73, 113, 127, 131, 137, 151, 173, 211, 223, 257, 271, 277, 281, 311, 317, 431, 457, 523, 541, 547, 557, 577, 727, 757, 821, 853, 1117, 1151, 1171, 1187, 1217, 1223, 1277, 1427, 1451, 1481, 1511, 1523

Offset: 1

Author

Erich Leistenschneider (el(AT)erichl.net), Feb 01 2008

Keywords

• nonn
• base

Examples

			2531 is a member of this sequence because it is a prime number and the product of its digits is 2*5*3*1 = 30 and the sum of the digits of this result is 3+0 = 3, which is also a prime number.
		

Links

• Erich Leistenschneider, Table of n, a(n) for n = 1..4095
• Erich Lestenschneider's Article about this sequence (in Portuguese).
• Erich Leistenschneider, Program used to generate the sequence (Linux)
• Erich Leistenschneider, First 4095 numbers of the sequence

Crossrefs

Subsequence of A038618 (zeroless primes).

Programs

Maple

a:=proc(n) local dn,pr,dpr: dn:=convert(n,base,10): pr:=mul(dn[i],i=1..nops(dn)): dpr:=convert(pr,base,10): if isprime(n)=true and isprime(add(dpr[j],j= 1..nops(dpr)))=true then n else end if end proc: seq(a(n),n=1..1600); # Emeric Deutsch, Mar 01 2008

Mathematica

Select[Prime[Range[300]],PrimeQ[Total[IntegerDigits[Times@@ IntegerDigits[#]]]]&] (* Harvey P. Dale, Dec 15 2011 *)

PARI

isok(p) = isprime(p) && isprime(sumdigits(vecprod(digits(p)))); \\ Michel Marcus, Jan 16 2019