# [seqfan] Re: Prime of the form 4*p + 3

M. F. Hasler oeis at hasler.fr
Mon Mar 16 00:46:58 CET 2020

```Even the twin prime, Goldbach, Legendre's, Collatz... conjectures are still
unproved in spite of most overwhelming numerical evidence...
--
Maximilian

On Sun, Mar 15, 2020, 07:08 Frank Adams-watters via SeqFan <
seqfan at list.seqfan.eu> wrote:

> Even the existence of infinitely many Sophie Germain primes is an unproved
> conjecture.
>
>
>
> -----Original Message-----
> From: zbi74583_boat <zbi74583_boat at yahoo.co.jp>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Sun, Mar 15, 2020 12:34 am
> Subject: [seqfan] Re: Prime of the form 4*p + 3
>
>     Hi  Robert
>     Thanks for telling me the information
>    I wish that someone will prove it, especially some smart Mathematician
> will prove in future the pair  {p, 2*p + 1}  which are both Sophie
>    German Primes exist infinitely
>     Because  if the proof exists then it is possible to prove  {3, -1}
> Amicable Pair exist infinitely many, though
>     the following is unsolved problem
>            Does Amicable Pair exist infinitely many ?
>
>
>     Yasutoshi
>
>      ----- Original Message -----
>  From: "israel at math.ubc.ca" <israel at math.ubc.ca>
>  To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>  Date: 2020/3/11, Wed 22:46
>  Subject: [seqfan] Re: Prime of the form 4*p + 3
>
> Look up "Dickson's conjecture". AFAIK there is no known proof of any case
> of Dickson's conjecture with k > 1: the closest is Yitang Zhang's proof
> that there is some d (with an explicit bound) such that p and p+d are both
> prime infinitely often.
>
> Cheers,
> Robert
>
> On Mar 11 2020, zbi74583_boat at yahoo.co.jp wrote:
>
> >  Does anyone know the proof
> > that  Prime of the form  4*p + 3  exist infinitely ?
>
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```