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May 13th, 2018, 04:31 PM   #1
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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 06:39 PM.
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May 13th, 2018, 06:36 PM   #2
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If there are finitely many primes of the form 4n-1, let m be their product. Is 4m-1 prime?
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May 13th, 2018, 06:58 PM   #3
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Quote:
Originally Posted by Mahmoudi Nima View Post
I need it badly.
Why?
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May 13th, 2018, 10:05 PM   #4
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Why?
What do you mean by figment?
It's a homework
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May 13th, 2018, 10:08 PM   #5
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Originally Posted by skipjack View Post
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 10:41 PM.
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May 13th, 2018, 10:44 PM   #6
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As 4m-1 isn't prime, what is the form of the primes in its factorization?
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May 13th, 2018, 11:22 PM   #7
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Originally Posted by skipjack View Post
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 11:25 PM.
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May 14th, 2018, 08:13 AM   #8
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Are you okay? How can 4m-1 be even, given that 4m is even?
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May 14th, 2018, 09:50 AM   #9
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Oops, brainfart. It was quite late.
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May 14th, 2018, 10:05 AM   #10
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Phewwwww.......
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