I search a prime number of the form $$4891625\cdots $$ emerging by concating the perfect powers $p>1$ upto some specific limit $L$ With $L=529$, we get a number splitting into a $31$ and a $48$ digit-prime, so we have no forced small factors. According to my calculation, such a prime must have more than $19\ 000$ digits.

Does a prime of the desired form exist ?

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    $\begingroup$ a definite maybe $\endgroup$ – Hagen von Eitzen May 13 '18 at 10:47
  • $\begingroup$ There shouldn't be an $8$ in your prime, it's a typo. $\endgroup$ – Lukas Kofler May 13 '18 at 10:51
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    $\begingroup$ @LukasKofler I don't understand. Why should a prime not contain digit $8$ ? $\endgroup$ – Peter May 13 '18 at 10:52
  • $\begingroup$ Sorry, I only meant the first number you wrote: it should be $491625 \dots$. $\endgroup$ – Lukas Kofler May 13 '18 at 10:53
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    $\begingroup$ @LukasKofler I concatenate the perfect powers, not only the perfect squares. $8$ is a cube, so it is written down as well. $\endgroup$ – Peter May 13 '18 at 10:54

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