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 April 16th, 2018, 09:14 AM #1 Senior Member   Joined: Dec 2015 From: somewhere Posts: 640 Thanks: 91 Prime or not ? Is $\displaystyle 14n-3$ prime for each positive integer $\displaystyle n$ if so then how to prove it ?
 April 16th, 2018, 09:35 AM #2 Senior Member   Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 $\dfrac{14n - 3}{3} = 14 * \dfrac{n}{3} - 1.$ Do you suppose there are some positive integers evenly divisible by 3?
 April 16th, 2018, 10:58 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,969 Thanks: 2222 It's easier to disprove it: 14 × 2 - 3 = 5², which is composite. One can similarly deal with $14^n - 3$.
 April 16th, 2018, 01:19 PM #4 Global Moderator   Joined: May 2007 Posts: 6,823 Thanks: 723 There is no simple polynomial formula for primes. Thanks from JeffM1
 April 16th, 2018, 04:35 PM #5 Global Moderator   Joined: Dec 2006 Posts: 20,969 Thanks: 2222 Where "simple" means what?
April 16th, 2018, 08:34 PM   #6
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Quote:
 Originally Posted by idontknow Is $\displaystyle 14n-3$ prime for each positive integer $\displaystyle n$ if so then how to prove it ?
So you did not even bother to check as far as $n=2$ before asking about this?

April 16th, 2018, 10:29 PM   #7
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Quote:
 Originally Posted by skipjack Where "simple" means what?
Any. Mathman meant to say that there is no polynomial that produces only primes. Simple or not. I think it was a rhetorical imprecision, not a mathematical one. There is no such thing as a simple polynomial, it's not a definition I've ever heard. So mathman was using simple as an intensifier ... a simple polynomial, as in a mere polynomial. No mere polynomial could do what you want. No simple polynomial etc.

That's how I interpreted mathman's remark. Simple as in a rhetorical flourish; not at all as specifying some subset of all the polynomials.

Last edited by Maschke; April 16th, 2018 at 10:32 PM.

 April 17th, 2018, 11:46 AM #8 Senior Member   Joined: Dec 2015 From: somewhere Posts: 640 Thanks: 91 How can we show that the prime formula exists or not ? In math we always must prove the existence first
April 17th, 2018, 12:46 PM   #9
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Quote:
 Originally Posted by mathman There is no simple polynomial formula for primes.
Polynomial with integer coefficients.

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