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

zak seidov zakseidov at yahoo.com
Thu Jul 22 07:31:42 CEST 2010

```Also see just submitted

%S A175600 53,149,293,389,773,1109,1493,1637,1733,2309,2693,2837,
%N A175600 Primes of form 4n+1 with n = pythagorean prime.
%C A175600 "Double-pythagorean" primes: primes of form 4n+1 with n = prime of form 4m+1.
%e A175600 53=A002144(7)= 4*13+1, 13=A002144(2)
%Y A175600 Cf. A002144 Pythagorean primes: primes of form 4n+1, A005098 Numbers n such that 4n+1 is prime.
%K A175600 nonn
%O A175600 1,1
%A A175600 Zak Seidov (zakseidov(AT)yahoo.com), Jul 22 2010

--- On Thu, 7/22/10, zak seidov <zakseidov at yahoo.com> wrote:

> From: zak seidov <zakseidov at yahoo.com>
> Subject: [seqfan]  A127589 Primes of the form 16k+5: prime k(?)
> To: "seqfaneu" <seqfan at seqfan.eu>
> Date: Thursday, July 22, 2010, 1:24 AM
> 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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>

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