A057876 Primes p with the following property: let d_1, d_2, ... be the distinct digits occurring in the decimal expansion of p. Then for each d_i, dropping all the digits d_i from p produces a prime number. Leading 0's are not allowed.

23, 37, 53, 73, 113, 131, 137, 151, 173, 179, 197, 211, 311, 317, 431, 617, 719, 1531, 1831, 1997, 2113, 2131, 2237, 2273, 2297, 2311, 2797, 3137, 3371, 4337, 4373, 4733, 4919, 6173, 7297, 7331, 7573, 7873, 8191, 8311, 8831, 8837, 12239, 16673, 19531

Offset: 1

Author

Patrick De Geest, Oct 15 2000

Keywords

• nonn
• base

Examples

			1531 gives primes 53, 131 and 151 after dropping digits 1, 5 and 3.
A larger example 1210778071 gives primes 12177871, 2077807, 110778071, 1210801 and 121077071 after dropping digits 0, 1, 2, 7 and 8.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A057877-A057883, A051362, A034302-A034305.

Programs

Maple

filter:= proc(n) local L,d,Lp;
  if not isprime(n) then return false fi;
  L:= convert(n,base,10);
  for d in convert(L,set) do
    Lp:= subs(d=NULL,L);
    if Lp=[] or Lp[-1] = 0 then return false fi;
    if not isprime(add(Lp[i]*10^(i-1),i=1..nops(Lp))) then return false fi;
  od;
  true
end proc:
select(filter, [seq(i,i=13..20000,2)]); # Robert Israel, Jul 13 2018

Extensions

Name edited by Robert Israel, Jul 13 2018