# [seqfan] Re: A127589 Primes of the form 16k+5: prime k(?)

Artur grafix at csl.pl
Thu Jul 22 08:04:31 CEST 2010

```Thank you for finding error!
Should be

All these prime numbers are the sum of two squares and if k is also prime is a sum
of two squares. Proof (Artur Jasinski): according to Fermat's theorem
all prime numbers of the form 4n+1 are sum of two squres. Also 16k+5
= 4(4k+1)+1.

Best wishes
Artur

zak seidov pisze:
> Values of k in A127589 are not always a sum of two squares (see A127590),
>
> and %C A127589 may be shortened to:
>
> %C A127589 All these prime numbers are the sum of two squares.
>
> Or even better,
> %C A127589 may be totally omitted (?)
>
> Zak
>
> %%%%%%%%%%% as at present in OEIS %%%%%%%%%%%%%%%%%%%%%
> %S A127589 5,37,53,101,149,181,197,229,277,293,373,389,421,613,661,677,709,757,
> %N A127589 Primes of the form 16k+5.
> %C A127589 All these prime numbers are the sum of two squares and k is also a sum
>                of two squares. Proof (Artur Jasinski): according to Fermat's theorem
>                all prime numbers of the form 4n+1 are sum of two squres. Also 16k+5
>                = 4(4k+1)+1.
>
> %S A127590 0,2,3,6,9,11,12,14,17,18,23,24,26,38,41,42,44,47,48,51,53,62,63,66,68,
> %N A127590 Numbers n such that 16n+5 is prime.
>
>
>
>
>
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>
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>
>

```