A different approach to prime numbers

In summary, a different approach to prime numbers is to take the difference of two products of primes. If each prime factor up to the nth prime factor is a factor of one of the two products, then that difference is a prime.
  • #1
kureta
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0
[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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  • #2
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 that's 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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  • #3
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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  • #4
Oh yes, it's something to do with group theory, but I forget its name off the top of my head. I had the option of studying that as my 3rd year project but ended up going with the transfer homomorphism, see if I can find my notes somewhere and fine the name for you.
 

1. What is the different approach to prime numbers?

The different approach to prime numbers is a method of finding and identifying prime numbers that differs from the traditional method. It involves using a combination of algorithms and mathematical properties to efficiently determine whether a number is prime or not.

2. How does this approach differ from the traditional method of finding prime numbers?

The traditional method of finding prime numbers involves systematically checking each number to see if it is divisible by any number other than itself and one. However, the different approach uses more advanced mathematical concepts and algorithms to quickly determine the primality of a number.

3. What are the benefits of using this different approach to prime numbers?

One of the main benefits of using this approach is that it is much faster and more efficient compared to the traditional method. It also allows for larger prime numbers to be identified and can be easily adapted to work with different number systems and bases.

4. Are there any limitations to this different approach?

Like any method, there are limitations to this approach. It may not be suitable for all types of numbers, and there can be instances where the traditional method may be more effective. Additionally, this approach may require a deeper understanding of mathematical concepts and algorithms.

5. How has this different approach to prime numbers impacted the field of mathematics?

This approach has greatly advanced the study of prime numbers and has led to new discoveries and insights. It has also opened up possibilities for further research and applications in other areas of mathematics.

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