October 14th, 2016, 04:08 PM  #1 
Newbie Joined: Oct 2016 From: United States Posts: 3 Thanks: 0  Prime number theory
Prime number question: Is the following prime number formula/theory viable: P = N – {2(N + 1)} – {3(2N + 1)} – {(6N1)((6N1) + (12N1) + (18N1) + (24N1)+ …(6(∞)N1))}  {(6N+1)((6N1) + (12N1) + (18N1) + (24N1)+ …(6(∞)N1))}  {(6N+1)((6N+1) + (12N+1) + (18N+1) + (24N+1)+…(6(∞)N+1))} , where P is all primes, N is all natural whole numbers, and P≠ 0,1.? 
October 14th, 2016, 06:46 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,936 Thanks: 2265 Math Focus: Mainly analysis and algebra 
Are you suggesting: 1) that this formula produces a prime for every natural number N; and 2) that the formula generates every prime number? It sounds unlikely to me, but it's not my field. How many natural numbers have you checked your formula for? Mobel is a number theorist on here who wishes to encourage creativity. I hope he has something useful to say on this. Last edited by skipjack; October 16th, 2016 at 01:57 AM. 
October 14th, 2016, 07:14 PM  #3 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,320 Thanks: 450 Math Focus: Yet to find out.  
October 15th, 2016, 07:52 PM  #4 
Newbie Joined: Oct 2016 From: United States Posts: 3 Thanks: 0 
I do believe (yes) that 1) this formula produces a prime for every natural number N; and 2) that the formula generates every prime number. But I will leave it up to the experts here to verify or discount the formula. 
October 16th, 2016, 04:29 AM  #5 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,936 Thanks: 2265 Math Focus: Mainly analysis and algebra 
How many natural numbers have you tested to verify that they produce primes? How many primes numbers have you tested to verify that they are produced by produce natural numbers? What do you mean by $6(\infty)N1$? The formula has three lines, can you explain how I generate a value for each line in order to combine them? Last edited by v8archie; October 16th, 2016 at 04:35 AM. 
October 16th, 2016, 05:21 AM  #6 
Newbie Joined: Aug 2015 From: Montenegro (Podgorica) Posts: 12 Thanks: 2 
6(∞)N 1 he means the big number that is a multiple of 6 minus 1.

October 16th, 2016, 06:57 AM  #7 
Newbie Joined: Aug 2015 From: Montenegro (Podgorica) Posts: 12 Thanks: 2 
this can be interesting because of the fact that every prime number is multiple of 6 minus or plus 1, but i think this formula is not well written and organized.

October 17th, 2016, 05:49 AM  #8 
Newbie Joined: Oct 2016 From: United States Posts: 3 Thanks: 0 
It is probably not well written and organized, I agree. With the tables I have concocted, I have simply discovered that not only do all primes exist within the parameters of 6N±1 (after the numbers 2 and 3), but that all non primes within 6N±1 are simply all of the multiples of all of those numbers within 6N±1 (without exception). My formula is an attempt (albeit lame, perhaps) of showing that all primes are elicited by removing the sets of those multiples of 2, and 3, and 6N±1. If mine is not correctly written, surely one with greater expertise than mine can accomplish it. 

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