A217064 Primes that remain prime when a single "5" digit is inserted between any two adjacent decimal digits.

11, 17, 47, 71, 83, 89, 149, 167, 179, 251, 257, 293, 347, 359, 383, 419, 461, 467, 491, 557, 563, 569, 653, 773, 911, 1193, 1217, 1277, 1451, 1559, 1667, 1823, 1901, 2243, 2309, 2357, 2579, 2657, 2999, 3527, 3533, 4289, 5051, 5351, 5501, 5843, 6089, 6551, 6581

Offset: 1

Author

Paolo P. Lava, Sep 26 2012

Keywords

• nonn
• base

Examples

			290183 is prime and also 2901853, 2901583, 2905183, 2950183 and 2590183.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..500 (First 140 terms from Paolo P. Lava)

Crossrefs

Cf. A050674, A050711-A050719, A069246, A159236, A215417, A215419-A215421, A217044-A217047, A217062, A217063, A217065

Programs

Maple

with(numtheory);
A217064:=proc(q,x)
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)+10^i*x;  if not isprime(c) then ok:=0; break; fi; od;
    if ok=1 then print(ithprime(n)); fi; od; end:
A217064(1000000,5);

Mathematica

Select[Prime[Range[5,1000]],AllTrue[FromDigits/@Table[ Insert[ IntegerDigits[ #],5,n],{n,2,IntegerLength[#]}],PrimeQ]&] (* Harvey P. Dale, Feb 20 2022 *)

PARI

is(n)=my(v=concat([""], digits(n))); for(i=2, #v-1, v[1]=Str(v[1], v[i]); v[i]=5; if(i>2, v[i-1]=""); if(!isprime(eval(concat(v))), return(0))); isprime(n) \\ Charles R Greathouse IV, Sep 26 2012