August 16th, 2017, 02:32 AM  #21 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 234 
If $ \ \ 5 \ \ $ was not a prime then all primes greater than $ \ \ 3 \ \ $ would be of the form $ \ \ 6n + 1 \ \ $ Unfortunately , $ \ \ 5 \ \ $ is prime. 
August 16th, 2017, 05:22 AM  #22 
Banned Camp Joined: Dec 2012 Posts: 1,028 Thanks: 24 
Primes are linear or bifidus: use 3n+1 and 3n+2 Last edited by complicatemodulus; August 16th, 2017 at 05:36 AM. 
August 29th, 2017, 09:26 AM  #23 
Senior Member Joined: Mar 2015 From: England Posts: 204 Thanks: 5 
After looking into trying to find a predictable sequential pattern for Primes in the last seven months or so, after all the research, I now believe that they are Statistical Distributions and that's how the Riemann Hypothesis works. This hypothesis is important in other areas of Maths. There for I believe it would be impossible for Primes to have a sequential pattern, because that would make them not random. And this may sound confrontational but people like Mario'D'Altaire who claim they have found the pattern are not helpful and are this generations circle squarers in the Maths world. 
August 29th, 2017, 09:29 AM  #24 
Senior Member Joined: Mar 2015 From: England Posts: 204 Thanks: 5 
Also a quick way to explain the Ulamm's Spiral which turns into the Sack's Spiral he likes so much for his misleading video is this. Pronic numbers 1 2 3 4 every 1 and 4 is not a multiple of 6. And then you start on from 4 as 1. This works because all Primes are close to multiples of 6. 
August 29th, 2017, 10:40 AM  #25  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,697 Thanks: 2681 Math Focus: Mainly analysis and algebra  Quote:
I understood that there were an infinite number of prime pairs $(p,p+2)$ and these must necessarily be of the form $(6n1,6n+1)$.  
August 29th, 2017, 12:50 PM  #26  
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Quote:
That's still unproven.  
August 29th, 2017, 01:36 PM  #27 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 552  That is unclear. If 5 is composite, then there exist positive integers x and y such that x * y = 5. Can you prove that neither x nor y nor any combination of x and y that is an integer divides evenly into 11? Because we are in the dark about the arithmetic of x and y, such a proof strikes me as impossible. 
August 30th, 2017, 03:18 PM  #28 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 234  Well let me make it plausible If $ \ \ 5 \ \ $ was composite it would have to be divisible by $ \ \ 2 \ \ $ , $ \ \ 3 \ \ $ or $ \ \ 4 \ \ $ $ 6 \ \ $ has common factors with $ \ \ 2 \ \ $ , $ \ \ 3 \ \ $ and $ \ \ 4 \ \ $ So ... $ 6n + 5 \ \ $ would be factorable therefore not prime. No Sir , IF $ \ \ 5 \ \ $ was composite there would be no primes of the form $ \ \ 6n  1 $ $ 11 \ \ $ could be written as $ \ \ 6 \times 1 + 5 \ \ $ and then factored The important word here is IF Welcome back Hoempa , missed you buddy ... Easy exercise... Prove that $ \ \ 6 \times 12 + 5 \ \ $ is composite without multiplying it out to get $ \ \ 77 \ \ $ You are not allowed to use $ \ \ 77 \ \ $ in any way. Last edited by agentredlum; August 30th, 2017 at 03:49 PM. 
August 30th, 2017, 04:44 PM  #29 
Senior Member Joined: Aug 2012 Posts: 2,426 Thanks: 760 
It seems perfectly plausible to me. If 5 were not prime then I would be the Pope. That is a logically true statement. In fact every proposition would be true, including the one suggested by the OP. I truly don't understand the sense of trying to reason mathematically on the assumption that 5 is not prime. What does that even mean? What are its prime factors? 
August 30th, 2017, 05:22 PM  #30  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 234  Quote:
I made a simple statement and then followed the implications. You're mocking and that's not nice  

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