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 April 16th, 2018, 10:14 AM #1 Senior Member   Joined: Dec 2015 From: Earth Posts: 833 Thanks: 113 Math Focus: Elementary Math Prime or not ? Is $\displaystyle 14n-3$ prime for each positive integer $\displaystyle n$ if so then how to prove it ? April 16th, 2018, 10:35 AM #2 Senior Member   Joined: May 2016 From: USA Posts: 1,310 Thanks: 552 $\dfrac{14n - 3}{3} = 14 * \dfrac{n}{3} - 1.$ Do you suppose there are some positive integers evenly divisible by 3? April 16th, 2018, 11:58 AM #3 Global Moderator   Joined: Dec 2006 Posts: 21,128 Thanks: 2336 It's easier to disprove it: 14 × 2 - 3 = 5², which is composite. One can similarly deal with $14^n - 3$. April 16th, 2018, 02:19 PM #4 Global Moderator   Joined: May 2007 Posts: 6,856 Thanks: 745 There is no simple polynomial formula for primes. Thanks from JeffM1 April 16th, 2018, 05:35 PM #5 Global Moderator   Joined: Dec 2006 Posts: 21,128 Thanks: 2336 Where "simple" means what? April 16th, 2018, 09:34 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, 11:29 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 11:32 PM. April 17th, 2018, 12:46 PM #8 Senior Member   Joined: Dec 2015 From: Earth Posts: 833 Thanks: 113 Math Focus: Elementary Math How can we show that the prime formula exists or not ? In math we always must prove the existence first April 17th, 2018, 01:46 PM   #9
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Quote:
 Originally Posted by mathman There is no simple polynomial formula for primes.
Polynomial with integer coefficients. Tags prime Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Kosxon New Users 2 July 20th, 2017 04:08 PM momo Number Theory 4 June 3rd, 2017 04:29 PM blind887 Algebra 2 April 12th, 2017 03:35 AM M_B_S Number Theory 59 October 6th, 2014 12:52 AM momo Number Theory 14 September 26th, 2008 08:21 AM

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