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

[Frank Adams-watters]

Even the existence of infinitely many Sophie Germain primes is an unproved conjecture.

Franklin T. Adams-Watters


-----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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