# [seqfan] Re: Primes of the form 8n + 7 or -x + 4xy + 4y^2

Neil Sloane njasloane at gmail.com
Sun Nov 13 20:33:12 CET 2016

```Al,  I agree with your reasoning, and I will edit the two sequences as you
suggest.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Email: njasloane at gmail.com

On Sun, Nov 13, 2016 at 2:23 PM, Alonso Del Arte <alonso.delarte at gmail.com>
wrote:

> I am now convinced that A007522, primes of the form 8n + 7, and A141175,
> primes of the form -x + 4xy + 4y^2, are indeed the same sequence.
>
> If both x and y are even, then it doesn't matter, -x + 4xy + 4y^2 gives us
> a composite even number. If x is even but y is odd then the formula still
> gives us a composite even number.
>
> If y is even, then 4xy + 4y^2 is a multiple of 8. With y even and x odd, we
> see that x^2 = 1 mod 8, which "flips over" to -x^2 = 7 mod 8. Therefore,
> primes of the form -x + 4xy + 4y^2 are a trivial, not proper, subset of
> primes of the form 8n + 7.
>
> This is correct and complete, right? Given that A141175 has been in the
> OEIS for almost a decade, it should be labeled a duplicate and have its
> relevant information not already in A007522 copied over to the older entry?
>
> Al
>
> --
> Alonso del Arte
> Author at SmashWords.com
> <https://www.smashwords.com/profile/view/AlonsoDelarte>
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>

```