# A different approach to prime numbers

## Main Question or Discussion Point

[SOLVED] A different approach to prime numbers

i read something about choosing a finite set of numbers as primes and deriving the other numbers from aforementioned set so that every number is obtained by multiplying primes (the numbers you choose to be prime in your system) in every possible combination. then looking for a realtion between these primes and the numbers they generate. does someone know this method and who found it? and sorry for my bad english.

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Well of course, suppose you take the difference of two products of primes, and if each prime factor up to the nth prime factor is a factor of one of the two products. If the two products are coprime and the difference between these products is less than P(n)^2, then that difference is a prime. To me thats what your question is about. For instance 3*7 - 5*2 = 11; and 11 must be prime since 21 and 10 are coprime, the two products contain all prime factors up to 7 and 11 < 49. Each of the 11 primes between 7 and 49 can be represented in some way as such a difference. Is this a way to fine large primes? No since the size of the resulting products becomes too large to reasonably compute and it can not be easily determing what grouping will create a difference < n^2 and which is not a repeated difference.

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i think i couldn't explain myself. Let me put it this way. for example i choose {5,6,7} as my set of prime numbers. so in my system, natural numbers are 5,6,7,25,30,35,... because normally natural numbers are obtained by multiplying primes in every possible way. this is some kind of reverse engineering :) you already know the generating function of your primes because you provided them, once you find out the generating function of natural numbers of this system you can find a relation between these two functions and use this relation for approximations about real prime numbers. i am really sorry my english is not so good. especially in technical subjects.

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Zurtex