What are the search limits of factors of the numbers $10^{2^n}+1$?

Question

For the Fermat numbers, I know such a site which shows how far the factors of $2^{2^n}+1$ have been searched.

Is there somewhere a survey for the search limits for factors of the numbers $10^{2^n}+1$ ?

Answer 1

Prothsearch provides a factoring status for generalized Fermat numbers $10^{2^{n}}+1$.

It is also mentioned at the bottom of the page the smallest $n=31$ for which it is not known if $10^{2^{n}}+1$ is prime or composite.

Finally the search limits of GFN factors.

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Edit: I have finished primality tests for $n=24$ and $n=25$ , done with LLR by Jean Penné. Results:

$\large 10^{2^{24}}+1$ is not prime, thus composite with no known factors.

$\large 10^{2^{25}}+1$ is not prime, thus composite with no known factors.