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One and only (Posted on 2016-04-28) Difficulty: 2 of 5
There is only one prime p such that p! is p digits long.

Find it and prove its uniqueness.

No Solution Yet Submitted by Ady TZIDON    
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Possible approach | Comment 1 of 4

If it's true, then the answer is 23.

We can use x=Floor[10^n/n!] as a rough proxy for candidates. x rises to 2755 at n=9, n=10, then falls again.

If N is 25 or more, x=0. 22!, 23! and 24! return x in single figures, and all of those have their digit length equal to their value; but only 23 is prime.


Edited on April 28, 2016, 9:20 am
  Posted by broll on 2016-04-28 08:49:47

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