A215420 Primes that remain prime when a single digit 7 is inserted between any two consecutive digits or as the leading or trailing digit.

3, 19, 97, 433, 487, 541, 691, 757, 853, 1471, 2617, 2953, 4507, 6481, 7351, 7417, 8317, 13177, 31957, 42457, 46477, 47977, 50077, 59053, 71917, 73897, 74377, 77479, 77743, 77761, 79039, 99103, 175687, 220897, 271177, 360973

Offset: 1

Author

Paolo P. Lava, Aug 10 2012

Keywords

• nonn
• base

Examples

			59053 is prime as are 590537, 590573, 590753, 597053, 579053, and 759053.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..63 (all terms up to and including the 1 millionth prime)

Crossrefs

Cf. A215417, A215418, A215419, A215421.

Programs

Maple

A215420:=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:
A215420(1000,7);

Mathematica

Select[Prime[Range[31000]],AllTrue[FromDigits/@Table[Insert[ IntegerDigits[ #],7,n],{n,IntegerLength[#]+1}],PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 29 2020 *)