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An emirp is a prime such that a distinct prime is formed when its digits are reversed. According to Wikipedia (and its references), the largest known emirp is \[p:=10^{10006}+941992101 \times 10^{4999}+1\] discovered by Jens Kruse Andersen in 2007.

Question: Is there an emirp greater than $p$?

I'm asking since this number is quite small compared to the largest known palindromic prime $10^{290253}-2 \times 10^{145126}-1$ (ref.). This palindromic prime has been proved prime via the Brillhart-Lehmer-Selfridge test (Math. Comp. paper).

It seems to me, if we could find a class of numbers $x$, for which $x$ and the number formed by reversing its digits both have the form $k \times 2^n \pm 1$ with $2^n>k$, then we can use Brillhart-Lehmer-Selfridge (along with the Lucas-Lehmer-Riesel test) to find a much larger emirp (albeit with a lot of sieving and trial-and-error).

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If there is an emirp that big, then I'm willing to bet there is one that is bigger. Is your question whether there is a bigger known emirp? Is your question whether it is known that bigger ones exist? –  Gerry Myerson Oct 10 '12 at 4:49
    
Mostly, "is there one known" and if not "let's find one!" –  Douglas S. Stones Oct 10 '12 at 4:52

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