[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
https://mathworld.wolfram.com/AmicableQuadruple.html
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.
Franklin T. Adams-Watters
-----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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