Unique Relationship to find prime numbers

TheDude · 2012-06-06 05:21:12

It's interesting, but your method could be improved to produce all odd numbers except the primes with a single formula. Instead of starting from x = 6y + 5 and x = 6y + 7, use x = 2y + 1. You eventually get a formula of

n = 4qb + 2b + 4pq + 2p + 2q + 1

Where b, p, q are integers and 0 < b, q and 0 <= p

hasaneweidah · 2012-06-06 05:26:15

Wow very cool, did you improved it?

TheDude · 2012-06-06 05:31:54

I just took your basic idea and modified it. The equations you used, x = 6y + 5 and x = 6y + 7, simply generate all odd numbers except those divisible by 3. But the equation x = 2y + 1 generates all odd numbers. This has two benefits: 1) You don't have to check if a number is missing from the list because it's divisible by 3 to make sure it is prime, and 2) You only have one possibility for m and a: m = 2p + 1 and a = 2q + 1. This lets you generate your list from one formula instead of four.

hasaneweidah · 2012-06-06 05:34:47

It's great work. Would you like to write it in the form of article with your name and I will add it to my search as your improvement to the equations?

TheDude · 2012-06-06 06:09:04

You can take credit for it, you did the hard part and I'm not interested in publishing or anything like that.

hasaneweidah · 2012-06-06 06:17:11

OK. just give me your name

bobbym · 2012-06-06 07:28:15

Hi;

So

it is easy now to see that n is always odd and composite.

TheDude · 2012-06-06 07:39:03

Indeed, and also readily apparent that all composite odd numbers are covered.

Edit: In fact, you can even simplify it further to (2p + 1)(2q + 1) = 4pq + 2p + 2q + 1, 0 < p, q.

Last edited by TheDude (2012-06-06 07:42:01)

hasaneweidah · 2012-06-06 08:08:30

TheDude and bobbym very nice work.

TheDude I added it into search just I want to write your name so please send it to my e-mail or write it here.

hasaneweidah · 2012-06-20 10:02:44

bobbym and The dude, I have reached to general equation that gives all prime numbers only.

14.0zz0/2012/06/20/21/961041611

before 14 add 'www'

after 0zz0 add '.com'

and after 961041611 add '.png'

bobbym · 2012-06-21 00:23:36

Hi hasaneweidah;

I am getting a DNS error, when I try that link.

anonimnystefy · 2012-06-21 05:06:31

Hi bobbym

Maybe you typed it out wrong. It should be:

www14.0zz0.com/2012/06/20/21/961041611.png

hasaneweidah · 2012-06-21 05:12:06

sorry guys, it's wrong approach. But I will do my best to reach to the final equation

Good luck for you ,,,

bobbym · 2012-06-21 15:44:29

Hi anonimnystefy;

Thanks for the link but there are still some kinks to iron out in that equation.

Math Is Fun Forum

#26 2012-06-06 05:21:12

Re: Unique Relationship to find prime numbers

#27 2012-06-06 05:26:15

Re: Unique Relationship to find prime numbers

#28 2012-06-06 05:31:54

Re: Unique Relationship to find prime numbers

#29 2012-06-06 05:34:47

Re: Unique Relationship to find prime numbers

#30 2012-06-06 06:09:04

Re: Unique Relationship to find prime numbers

#31 2012-06-06 06:17:11

Re: Unique Relationship to find prime numbers

#32 2012-06-06 07:28:15

Re: Unique Relationship to find prime numbers

#33 2012-06-06 07:39:03

Re: Unique Relationship to find prime numbers

#34 2012-06-06 08:08:30

Re: Unique Relationship to find prime numbers

#35 2012-06-20 10:02:44

Re: Unique Relationship to find prime numbers

#36 2012-06-21 00:23:36

Re: Unique Relationship to find prime numbers

#37 2012-06-21 05:06:31

Re: Unique Relationship to find prime numbers

#38 2012-06-21 05:12:06

Re: Unique Relationship to find prime numbers

#39 2012-06-21 15:44:29

Re: Unique Relationship to find prime numbers

Board footer