Proof of infinitude of primes whose reversal in base 10 is also prime Is there any proof of infinitude of 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]))] 

 A: The answer is: no proof is known at this time, for any base, but it is suspected that a proof exists (it should be reasonably easy to give a density under the "standard hypotheses").
A: Now, thinking about this a bit, let's say $f$ is the function that reverses the digits, so that $f(n)$ is the number that has the digits of $n$ in base 10 reversed. I think that when estimating $$|\{n \leq x: n,f(n) \mbox{ simultaneously prime}\}|,$$
then for each prime $p$, maybe you'll have to estimate the number of solutions to 
$$
nf(n) \equiv 0 \bmod p,
$$
where $n \in \mathbb{Z}/p\mathbb{Z}$. This is similar to like when estimating the twin prime constant (but I'm not claiming that the whole thing goes through the same way). The problem is that $f(n)$ is not so straightforward like $n+2$ is.
For $p=3$, at least $f(n) \equiv n \bmod 3$, so that is ok. $p=11$ is also not too bad. For other $p$, it doesn't seem so straightforward.
In fact, it's not even as straightforward as this, because for $n,f(n)\in \mathbb{Z}$, when one fixes $n \bmod p$, $f(n) \bmod p$ is not fixed in general. The point is just that I think one might have to estimate the probability that $p\nmid f(n)\in \mathbb{Z}$, given that $p\nmid n\in \mathbb{Z}$.
A: Hello all,
I must be overlooking something, but I wonder if the systems $\Psi:\mathbb{Z}^d\rightarrow \mathbb{Z}^t$ in the Green-Tao paper "Linear Equations in Primes" could apply to this question. 
