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May 13th, 2018, 03:31 PM  #1 
Newbie Joined: Apr 2018 From: Algeria Posts: 3 Thanks: 0 Math Focus: Analys  Primes of the form (4n1)
I would like help to prove that primes of the form (4n1) or (6n1) are not finite in number. I'll try to assume that primes of the form (4n1) are finite so there is k in N where (4k1) is the largest prime of this form. So for any m in N larger than k, (4m1) is not prime. So there is a prime p which divides (4m1). Then I didn't reach anywhere. I need it badly. Thanks. Last edited by skipjack; May 13th, 2018 at 05:39 PM. 
May 13th, 2018, 05:36 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,026 Thanks: 2257 
If there are finitely many primes of the form 4n1, let m be their product. Is 4m1 prime?

May 13th, 2018, 05:58 PM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039  
May 13th, 2018, 09:05 PM  #4 
Newbie Joined: Apr 2018 From: Algeria Posts: 3 Thanks: 0 Math Focus: Analys  
May 13th, 2018, 09:08 PM  #5  
Newbie Joined: Apr 2018 From: Algeria Posts: 3 Thanks: 0 Math Focus: Analys  Quote:
Thanks for any where. Last edited by skipjack; May 13th, 2018 at 09:41 PM.  
May 13th, 2018, 09:44 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 21,026 Thanks: 2257 
As 4m1 isn't prime, what is the form of the primes in its factorization?

May 13th, 2018, 10:22 PM  #7 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,690 Thanks: 2669 Math Focus: Mainly analysis and algebra  Don't you need the product of all primes up to and including the greatest prime of the form (4n1)? (4m1) (as defined by you) is an even number.
Last edited by v8archie; May 13th, 2018 at 10:25 PM. 
May 14th, 2018, 07:13 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 21,026 Thanks: 2257 
Are you okay? How can 4m1 be even, given that 4m is even?

May 14th, 2018, 08:50 AM  #9 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,690 Thanks: 2669 Math Focus: Mainly analysis and algebra 
Oops, brainfart. It was quite late.

May 14th, 2018, 09:05 AM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 
Phewwwww.......


Tags 
4n1, 4n1, form, number theory, primes 
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