A217044 Primes that remain prime when a single "2" digit is inserted between any two adjacent decimal digits.

17, 23, 29, 41, 53, 83, 89, 101, 113, 131, 137, 149, 251, 359, 401, 419, 443, 461, 647, 719, 797, 821, 863, 941, 1289, 1823, 2111, 2543, 3323, 3413, 4013, 4463, 4751, 5021, 5501, 5807, 6299, 6827, 7229, 7643, 7883, 8039, 8219, 8609, 8837, 9221, 9227, 9461, 9623

Offset: 1

Author

Paolo P. Lava, Sep 25 2012

Keywords

• nonn
• base

Examples

			9461 is prime and also 94621, 94261, 92461.
		

Links

• Bruno Berselli, Table of n, a(n) for n = 1..500 (first 123 terms from Paolo Lava)

Crossrefs

Cf. A050674, A050711-A050719, A069246, A159236, A215417, A215419-A215421, A217045-A217047, A217062-A217065.

Programs

Magma

[p: p in PrimesInInterval(11, 10000) | forall{m: t in [1..#Intseq(p)-1] | IsPrime(m) where m is (Floor(p/10^t)*10+2)*10^t+p mod 10^t}]; // Bruno Berselli, Sep 26 2012

Maple

with(numtheory);
A217044:=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:
A217044(100000,2)

Mathematica

Select[Prime[Range[5,1200]],And@@PrimeQ[FromDigits/@Table[ Insert[ IntegerDigits[ #],2,i],{i,2,IntegerLength[#]}]]&] (* Harvey P. Dale, Oct 09 2012 *)

PARI

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