A384953 First of three consecutive primes whose concatenations, both forward and backward, are primes.

313, 359, 383, 449, 619, 787, 827, 907, 1697, 2503, 2521, 2857, 3673, 3853, 4139, 4363, 4993, 5281, 5527, 5563, 5641, 5851, 6037, 6043, 6719, 7019, 7477, 9281, 10177, 10459, 13799, 14009, 15013, 15511, 17167, 17209, 19183, 19423, 20483, 20743, 21397, 21407, 25111

Offset: 1

Author

Robert Israel, Jun 13 2025

Keywords

• nonn
• base

Examples

			a(3) = 383 is a term because 383, 389 and 397 are consecutive primes and both 383389397 and 397389383 are prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A030469, A104328.

Programs

Maple

rcat:= proc(L) local x,i;
  x:= L[1];
  for i from 2 to nops(L) do
    x:= 10^(1+ilog10(x))*L[i] + x
  od;
  x
end proc:
fcat:= proc(L) local x,i;
  x:= L[1];
  for i from 2 to nops(L) do
    x:= 10^(1+ilog10(L[i]))*x + L[i]
  od;
  x
end proc:
P:= select(isprime,[seq(i,i=3..30000,2)]):
J:=  select(i -> isprime(rcat(P[i..i+2])) and isprime(fcat(P[i..i+2])), [$1..nops(P)-2]):
P[J];