A215419 Primes that remain prime when a single digit 3 is inserted between any two consecutive digits or as the leading or trailing digit.

7, 11, 17, 31, 37, 73, 271, 331, 359, 373, 673, 733, 1033, 2297, 3119, 3461, 3923, 5323, 5381, 5419, 6073, 6353, 9103, 9887, 18289, 23549, 25349, 31333, 32933, 33349, 35747, 37339, 37361, 37489, 47533, 84299, 92333, 93241, 95093, 98491, 133733, 136333, 139333

Offset: 1

Author

Paolo P. Lava, Aug 10 2012

Keywords

• nonn
• base

Examples

			18289 is prime and also 182893, 182839, 182389, 183289, 138289, 318289.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A215417, A069246, A215420, A215421

Programs

Maple

filter:= proc(n) local L,d,k,M;
if not isprime(n) then return false fi;
L:= convert(n,base,10);
d:= nops(L);
for k from 0 to d do
   M:= [seq(L[i],i=1..k),3,seq(L[i],i=k+1..d)];
   if not isprime(add(M[i]*10^(i-1),i=1..d+1)) then return false fi;
od;
true
end proc;
select(filter, [seq(i,i=3..2*10^5,2)]); # Robert Israel, Oct 09 2017

Mathematica

ins@n_:=Insert[IntegerDigits@n,3,#]&/@Range@(IntegerLength@n+1);
Cases[{#,FromDigits@#&/@ins@#}&/@ Cases[Range[11,70000],?PrimeQ], {,{?PrimeQ..}}][[All,1]] (* _Hans Rudolf Widmer, Dec 21 2023 *)