My Math Forum Primes of the form (4n-1)

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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 (4n-1) I would like help to prove that primes of the form (4n-1) or (6n-1) are not finite in number. I'll try to assume that primes of the form (4n-1) are finite so there is k in N where (4k-1) is the largest prime of this form. So for any m in N larger than k, (4m-1) is not prime. So there is a prime p which divides (4m-1). 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 4n-1, let m be their product. Is 4m-1 prime?
May 13th, 2018, 05:58 PM   #3
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Quote:
 Originally Posted by Mahmoudi Nima I need it badly.
Why?

May 13th, 2018, 09:05 PM   #4
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Quote:
 Originally Posted by Denis Why?
What do you mean by figment?
It's a homework

May 13th, 2018, 09:08 PM   #5
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Quote:
 Originally Posted by skipjack If there are finitely many primes of the form 4n-1, let m be their product. Is 4m-1 prime?
Then, I'll try it but I didn't get any contradiction.
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 4m-1 isn't prime, what is the form of the primes in its factorization?
May 13th, 2018, 10:22 PM   #7
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Quote:
 Originally Posted by skipjack If there are finitely many primes of the form 4n-1, let m be their product. Is 4m-1 prime?
Don't you need the product of all primes up to and including the greatest prime of the form (4n-1)? (4m-1) (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 4m-1 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 4n-1, 4n1, form, number theory, primes

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