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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 ?

Peter
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    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. – bsbb4 May 13 '18 at 10:51
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    @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 $491625 \dots$. – bsbb4 May 13 '18 at 10:53
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    @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
  • You're right, my bad! – bsbb4 May 13 '18 at 10:55
  • @HagenvonEitzen I do not expect that it can be proven that no such prime exists, so the only chance seems to be to find a prime. – Peter May 13 '18 at 10:59
  • Apparently, such a prime must have even more than $26\ 000$ digits – Peter May 13 '18 at 12:45
  • I also tried finding a prime. My calculations are now at $53\ 868$ digits and still no prime result. – pietfermat May 14 '18 at 02:33
  • @pietfermat Apparently, you have a very powerful computer/software. I and Enzo Creti search for a special prime for a long time, it would be nice if you would join in the search. https://math.stackexchange.com/questions/2635516/a-conjecture-about-numbers-of-the-form-10m2k%e2%88%9212k-1%e2%88%921-where-m-is – Peter May 14 '18 at 05:55

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