# Proof of infinitude of primes whose reversal in base 10 is also prime

Is there any proof of infinitude of http://oeis.org/A007500 primes.

If you want to generate them here is trivial and naive python program.

def is_prime(n):
i = 2
while i*i <= n:
if n%i == 0:
return False
i = i + 1
else:
return True

print [x for x in range(1,200) if is_prime(x) and is_prime(int(str(x)[::-1]))]

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This is called a palindromic prime. See the wikipedia page, the Wolfram page, and Prime Glossary page. (Unfortunately, not much seems to be known about this question.) – Srivatsan Oct 17 '11 at 19:59
Specifically, that link says "It is not known if there are infinitely many palindromic primes in base 10." But, that doesn't mean someone can't figure out a proof! – Graphth Oct 17 '11 at 20:10
I would guess that the $n^{th}$ palindromic prime might be of the order of $n (\log_e n)^2$ in any base (with some fluctuation around this since all bar the first and third can only start with 1, 3, 7 or 9). – Henry Oct 17 '11 at 21:08
@Henry: The $n(\log n)^2$ is very reasonable. The constant might need adjustment, because if $n$ is not divisible by $3$ or $11$, neither is its reversal. – André Nicolas Oct 17 '11 at 21:43
Paul Erdős said, allegedly, about the Collatz conjecture: "Mathematics is not yet ripe for such problems". I asked this question because I suspected this one to be one of "such problems". – Pratik Deoghare Oct 18 '11 at 2:13