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4n^2-3n-1 and 4n^2+3n-1

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  • Sren
    Those two formulas I found while I was working with exclusion lines in Ulams prime spiral. None of them have primes at least up to n=10000. Are there any who
    Message 1 of 2 , Mar 24, 2010
      Those two formulas I found while I was working with exclusion lines in Ulams prime spiral. None of them have primes at least up to n=10000.

      Are there any who have an explanation ?
    • Jack Brennen
      4n^2-3n-1 == (n-1)(4n+1) 4n^2+3n-1 == (n+1)(4n-1) Only way either one is prime is if one of the two cofactors is 1 or -1 and the other one is a prime. You can
      Message 2 of 2 , Mar 24, 2010
        4n^2-3n-1 == (n-1)(4n+1)
        4n^2+3n-1 == (n+1)(4n-1)

        Only way either one is prime is if one of the two cofactors is 1 or -1
        and the other one is a prime. You can quickly check all of those
        possibilities, and eliminate them all; thus, no primes of either form.



        Sren wrote:
        > Those two formulas I found while I was working with exclusion lines in Ulams prime spiral. None of them have primes at least up to n=10000.
        >
        > Are there any who have an explanation ?
        >
        >
        >
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