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

zbi74583_boat at yahoo.co.jp zbi74583_boat at yahoo.co.jp
Wed Mar 18 04:43:22 CET 2020

```    Hi  Franklin  Maximilian    It is right    Certainly  these unsolved problems are too difficult to solve    I tell you another too difficult theorem as follows
If  Mersenne Prime exist infinitely then Amicable Quadruple exist infinitely    [ Proof ]    Here is the factorization of Amicable Quadruple which I computed
It has Mersenne Prime as prime factor  so  the theorem is proved    But  I know the following is too difficult problem
Does Mersenne Prime exist infinitely ?
I give you  much easier unsolved problems  of Amicable Pair

Does Amicable Pair coprime to 210 exist ?
For example  coprime to 2  or  coprime to 6=2*3  or coprime to 30=2*3*5  exist
Here is the list of Amicable Pair coprime to 30
http://62.198.248.44/aliquot/apstat/apco30.txt
Does Amicable 7-tuple exist ?    Here is A233538     It has Amicable Triple to 6-tuple
http://62.198.248.44/aliquot/apstat/apco30.txt
I am sure these two problems are much easier and they must exist

Yasutoshi
----- Original Message -----

Date: 2020/3/15, Sun 18:04
Subject: [seqfan] Re: Prime of the form 4*p + 3

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

-----Original Message-----

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 -----

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

>  Does anyone know the proof
> that  Prime of the form  4*p + 3  exist infinitely ?

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