April 16th, 2018, 10:14 AM  #1 
Senior Member Joined: Dec 2015 From: iPhone Posts: 387 Thanks: 61  Prime or not ?
Is $\displaystyle 14n3$ 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: 1,306 Thanks: 549 
$\dfrac{14n  3}{3} = 14 * \dfrac{n}{3}  1.$ 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: 20,301 Thanks: 1971 
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: 6,684 Thanks: 659 
There is no simple polynomial formula for primes.

April 16th, 2018, 05:35 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,301 Thanks: 1971 
Where "simple" means what?

April 16th, 2018, 09:34 PM  #6 
Senior Member Joined: Sep 2016 From: USA Posts: 559 Thanks: 324 Math Focus: Dynamical systems, analytic function theory, numerics  
April 16th, 2018, 11:29 PM  #7 
Senior Member Joined: Aug 2012 Posts: 2,157 Thanks: 631  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: iPhone Posts: 387 Thanks: 61 
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 
Global Moderator Joined: May 2007 Posts: 6,684 Thanks: 659  

Tags 
prime 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Prime software? not gimps or prime grid.  Kosxon  New Users  2  July 20th, 2017 04:08 PM 
Primorial + prime = prime  momo  Number Theory  4  June 3rd, 2017 04:29 PM 
Pythagorean prime in every prime twin  blind887  Algebra  2  April 12th, 2017 03:35 AM 
For every prime (x+y) exist a prime (xy)  M_B_S  Number Theory  59  October 6th, 2014 12:52 AM 
If P is prime imply that a is prime  momo  Number Theory  14  September 26th, 2008 08:21 AM 