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

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• 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
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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 ?
• 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
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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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