A215417 Primes that remain prime when a single zero digit is inserted between any two adjacent digits.

11, 13, 17, 19, 37, 41, 53, 59, 61, 67, 71, 79, 89, 97, 109, 113, 131, 149, 191, 197, 227, 239, 269, 281, 283, 337, 367, 379, 383, 401, 421, 449, 457, 499, 503, 509, 587, 607, 673, 701, 719, 727, 739, 757, 809, 811, 887, 907, 929, 991, 1009, 1061, 1093, 1103

Offset: 1

Author

Paolo P. Lava, Aug 10 2012

Keywords

• nonn
• base

Examples

			399617 is prime and also 3996107, 3996017, 3990617, 3909617, 3099617.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..4300 (terms a(1)-a(372) from Paolo P. Lava, terms a(373)-a(700) from Vincenzo Librandi)

Crossrefs

Cf. A159236, A069246, A215419-A215421.

Programs

Maple

A215417:=proc(q)
local a,b,c,i,n,ok;
for n from 5 to q do
  a:=ithprime(n); b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od;
  a:=ithprime(n);ok:=1;
  for i from 1 to b-1 do
    c:=a+9*10^i*trunc(a/10^i); if not isprime(c) then ok:=0; break; fi;
  od;
  if ok=1 then print(ithprime(n)); fi;
od; end:
A215417(1000);

Mathematica

Select[Prime[Range[5,200]],And@@PrimeQ[Table[FromDigits[Insert[ IntegerDigits[ #],0,n]],{n,2,IntegerLength[#]}]]&] (* Harvey P. Dale, Feb 23 2014 *)

PARI

is(n)=my(v=concat([""], digits(n))); for(i=2, #v-1, v[1]=Str(v[1], v[i]); v[i]=0; if(i>2, v[i-1]=""); if(!isprime(eval(concat(v))), return(0))); isprime(n) \\ Charles R Greathouse IV, Sep 26 2012