[seqfan] Pythagorean primes and nexus primes

[Tomasz Ordowski]

Dear SeqFans!

Let's define:

Primes p = a^2+b^2 such that (a^p-b^p)/(a-b) is prime or (a^p+b^p)/(a+b) is
prime.

Conjecture: these are primes p = k^2+(k-1)^2 such that k^p-(k-1)^p is
prime.

There are probably no primes (a^p+b^p)/(a+b) for p = a^2+b^2 > 5.

Cf. https://oeis.org/history/view?seq=A321616&v=13

Maybe someone will prove it or disprove it.

Best regards,

Thomas
_________________________
 https://oeis.org/draft/A321616
My invitation to the Discussion.



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