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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](http://en.wikipedia.org/wiki/Palindromic_prime), [the Wolfram page](http://mathworld.wolfram.com/PalindromicPrime.html), and [Prime Glossary page](http://primes.utm.edu/glossary/xpage/PalindromicPrime.html). (Unfortunately, not much seems to be known about this question.)2011-10-17
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    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!2011-10-17
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    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).2011-10-17
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    @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.2011-10-17
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    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".2011-10-18
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    It is widely believed, but hopeless to prove, that there are infinitely many "repunit" primes, that is, primes whose digits are all ones. These would, of course, be examples of primes whose reversal is prime.2012-02-25
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    @PratikDeoghare: I don't have any reason to think this problem is nearly as hard as Collatz.2014-01-22
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    Maybe not. But its unsolved as of now. :)2014-01-24

0 Answers 0