# Does concatenating the perfect powers ever lead to a prime?

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 ?

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