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

Sun Mar 15 10:04:15 CET 2020

```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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