A088883 Primes which when concatenated with their reverse and incremented by 2 yield a new prime.

7, 19, 97, 109, 151, 163, 181, 193, 547, 709, 727, 733, 991, 1039, 1093, 1279, 1447, 1453, 1567, 1621, 1657, 1669, 1699, 1723, 1867, 5077, 5179, 5209, 5281, 5323, 5419, 5503, 5563, 5581, 5653, 5821, 5857, 5881, 7057, 7207, 7219, 7333, 7351, 7507, 7537

Offset: 1

Author

Chuck Seggelin, Oct 21 2003

Keywords

• base
• nonn

Comments

It appears that if concat(p,reverse(p))+2 is prime, then concat(p,reverse(p))-2 is not and vice versa. This was tested for the first 60000 primes.

Conjecture: All these primes are of the form 6*k + 1. - Davide Rotondo, Apr 29 2025

Examples

			109 is a term because (i) 109 is prime and (ii) when 109 is concatenated with its reverse (901) + 2, the result (109903) is prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Subsequence of A002476.

Cf. A067087 (concatenation of n-th prime and its reverse), A088884 (with decremented rather than incremented).

Programs

Maple

filter:= proc(n) local L,d,i,x;
  if not isprime(n) then return false fi;
  L:= convert(n,base,10);
  d:= nops(L);
  x:= add(L[-i]*(10^(i-1)+10^(2*d-i)),i=1..d)+2;
  isprime(x)
end proc;
select(filter, [seq(i,i=7 .. 10^4,6)]); # Robert Israel, Apr 29 2025

Mathematica

crpQ[n_]:=Module[{idn=IntegerDigits[n]},PrimeQ[FromDigits[ Join[ idn, Reverse[ idn]]]+2]]; Select[Prime[Range[1000]],crpQ] (* Harvey P. Dale, Apr 28 2014 *)