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Re: [PrimeNumbers] k^n -> (k^n) + (2n-1) = prime ?!

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  • Jack Brennen
    Note that there are some values of n for which (k^n)+(2*n-1) is NEVER prime. For instance, if n == 63, then: (k^n)+(2*n-1) == (k^63)+125 == (k^21)^3 + 5^3
    Message 1 of 2 , Jun 25, 2001
      Note that there are some values of n for which (k^n)+(2*n-1) is NEVER prime.
      For instance, if n == 63, then:

      (k^n)+(2*n-1) == (k^63)+125 == (k^21)^3 + 5^3

      Which of course is always composite, being divisible by (k^21)+5.

      On the other extreme, (k^4)+7 seems to be a (relatively) rich source of
      prime numbers... For 0 <= k <= 10000, there are 698 such primes,
      compared to about 312 predicted using the prime number theorem.
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