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Proof:[n^n]-[(n-1)^(n-1)] is a prime n=natural number

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Sorry to disappoint you but your assertion is false:

proof:[n^n]-[(n-1)^(n-1)] is a prime - 911fa9e.jpg

Posted on Apr 24, 2010

  • k24674 Apr 27, 2010

    It is cear from the screen capture that for n=9 9^9 -8^8 is divisible by 7, by 11 and by 13 because it is divisible by their product. So, you cannot declare that n^n-(n-1)^(n-1) is a prime number for all natural numbers.



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First prime number is 2, then 3, 5, 7, 11, 13, 17, 19,
To generate a list of prime numbers the Greek Eratoshenes used a method called now the sieve Eratosthenes.

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  4. Go through the whole list crossing out all the numbers that are multiple of 2, that is 4, 6, 8,10,12, ...
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  6. The next prime number is 3 since it was not crossed out as a multiple of 2. Circle 3.
  7. Go through the whole list crossing all the numbers that are multiples of 3, and which have not already been crossed out as multiples of 2 .
  8. Number 4 has been crossed out already.
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  10. Go through the whole list crossing all the numbers that are multiple of 5 and which have not been crossed out already as multiples of 2, or 3
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