Prime pattern

Zaneh

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Mar 14, 2019
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I have recently been looking at prime numbers and think I have found a pattern. I'm just wondering the best place to seek advice on something like this?
 

topsquark

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Feel free to start here. What's the pattern?

-Dan
 

Zaneh

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Ok. Im terrible at writing so hope this make sense. I've noticed that all prime numbers are a multiple of 2520, plus a prime less than 2520 (1 is the exception and must be included) will always be prime. For example 2539 is 2520 plus 19. 5059, 10099, 12619, 15139 are all prime and all multiples of 2520 plus 19. So from this I have done an addition grid with all primes up too 2520 (including 1) along the top, and all multiples of 2520 running down, now not all numbers on this grid are prime but it does show all possible primes. So from this I have concluded that to find out if a number ending in 1,3,7,9 is not prime all you have to do is find the closest lower number dividable by 2520, subtract that from your original number and if the result isn't a prime number less than 2520 than that number cannot be prime. Am I missing something here? I've tried it with a few numbers up too 9 digits and it works every time. And seeing as all primes are linked to 2520 and the addition of a prime less than 2520 would this not mean their is a pattern to prime numbers?
 

Zaneh

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I would just like to add that if you do take any number and do the process above and it ends up being a prime less than 2520 then that dosnt guarantee that that number is prime, but it does prove it is either prime or not prime. I've just started looking at primes so hopefully I can find a connection with the numbers that arnt prime after applying the above method.
 

ksdhart2

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If what you found was a real pattern, it would be very interesting, but alas it's just not meant to be. Here's one counter example: 2689 = 2520 + 169 = 2520 + 132. Also, a bit of oddness here:

...but it does prove it is either prime or not prime...
So, this process proves that an integer is an integer? :p
 

Zaneh

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Thanks for your reply. Yes I fully respect what your saying. But I mean more so in terms of numbers like 2541, 5061, 7581, 10101, are all numbers ending in 1. Now if you take 10101 and subtract its closest multiple of 2520 (10080) then the result is 21 which isn't prime making 10101 not prime. I'm sorry for my poor explanation, I havnt studied maths other than high school. My method dosnt prove what numbers will be prime but shows which ones won't?
 

Zaneh

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So basically if you take any numbers multiple of 2520 and add a number less than 2520 that isn't prime then the result will NEVER be prime. I think this may help with massive numbers in a sense, you won't have to start deviding it by any numbers to work out if their prime, with some you can just do this and know its not prime
 
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Zaneh

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Mar 14, 2019
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Take any number between 0 and 2520 that isnt prime and ends in 1,3,7,9. Now add it to any multiple of 2520 and the result can't be prime. Maybe this explains my thoughts better.
 
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