A215421 Primes that remain prime when a single digit 9 is inserted between any two consecutive digits or as the leading or trailing digit.

7, 19, 37, 41, 199, 239, 311, 587, 661, 941, 967, 1009, 1997, 4993, 4999, 5393, 5651, 6911, 9109, 9397, 9679, 9829, 19417, 20233, 22549, 27397, 29389, 31387, 39989, 71419, 71569, 90599, 91951, 95369, 97103, 98909, 99023, 160009, 225919, 267389, 313991, 328849

Offset: 1

Author

Paolo P. Lava, Aug 10 2012

Keywords

• nonn
• base

Examples

			31387 is prime and also 313879, 313897, 313987, 319387, 391387, 931387.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A215417-A215420

Programs

Maple

A215421:=proc(q,x)
local a,b,c,d,i,n,ok;
for n from 1 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 0 to b do
    c:=a+9*10^i*trunc(a/10^i)+10^i*x; if not isprime(c) then ok:=0; break; fi;
  od;
  if ok=1 then print(ithprime(n)); fi;
od; end:
A215421(1000,9);

Mathematica

Select[Prime[Range[30000]],AllTrue[FromDigits/@Table[Insert[ IntegerDigits[ #],9,n],{n, IntegerLength[ #]+1}],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 22 2016 *)