A128717 Primes that yield another prime if one adds either the sum of its digits or the product of its digits.

101, 103, 163, 233, 293, 307, 431, 499, 509, 563, 617, 701, 743, 1009, 1049, 1061, 1087, 1409, 1423, 1483, 1489, 1601, 1607, 1801, 1867, 2017, 2039, 2053, 2273, 2543, 2633, 2903, 3041, 3067, 3089, 3449, 3607, 4013, 4057, 4079, 4211, 4217, 4273, 4507

Offset: 1

Author

J. M. Bergot, Jun 27 2007

Keywords

• base
• easy
• nonn

Examples

			163 + (1+6+3) = 173, 163 + 1*6*3 = 181; 173 and 181 are prime numbers.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A048519.

Programs

Maple

filter:= proc(n) local S;
  S:= convert(n,base,10);
  isprime(n+convert(S,`+`)) and isprime(n+convert(S,`*`))
end proc:
A:= NULL:
p:= 2:
while p < 10000 do
  if filter(p) then A:= A, p fi;
  p:= nextprime(p)
od:
A; # Robert Israel, Jul 12 2017

Mathematica

Select[Prime[Range[500]], PrimeQ[ # + Plus @@ IntegerDigits[ # ]] && PrimeQ[ # + Times @@ IntegerDigits[ # ]] &]

PARI

isok(n) = isprime(n) && (isprime(n+sumdigits(n)) && ((d=digits(n)) && isprime(n+prod(k=1, #d, d[k])))); \\ Michel Marcus, Jul 12 2017

Extensions

Edited, corrected and extended by Stefan Steinerberger, Jul 14 2007