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

Alonso Del Arte alonso.delarte at gmail.com
Sun Nov 13 20:23:01 CET 2016

```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>
Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>

```