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**Primenumbers****Member**- Registered: 2013-01-22
- Posts: 141

To generate prime numbers;

A= All primes apart from 2 multiplied together up to prime x.

prime when <(the prime just above x) squared and >1This is because A is factorable by all possible factors apart from 2, and

isn't. Also is factorable by 2 and A isn't. The remainders from for primes up to x carry to the answer. A is multiplied by all odd no.'s so is odd and is even, generating an odd no. with no factors <itself other than 1.This concept is useful when trying to prove that there are an **infinite number of twin primes**;

A= All primes apart from 2 multiplied together up to prime x.

p= prime>x

r=p+1

m= any odd integer

I.e. remainder for 7 for ==1

=2

=4

=1

=2

=4

=1............

So when z is a prime it is not a composite so the remainder 1 for other primes <z has not repeated itself. So

will not be factorable by primes <p and will not be factorable by primes<p but will be factorable by 2.Therefore

and generates twin primes, just so long as they = a no. <(the prime just above x) squared and are >1.Example:

A=105

p=13

r=14

m=157

**"Time not important. Only life important."*** - The Fifth Element 1997*

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**googol****Member**- From: Delft, The Netherlands
- Registered: 2016-04-22
- Posts: 13

Cool very

The product of all prime numbers up to a certain prime is called a Primorial

In your post

Sometimes the algorithm also works when the result is larger than the next prime squared.

For example:

and

are both prime but much larger than 23 squared (529).

I am not sure this proves that there is an infinite number of twin primes. The algorithm often finds the same twin primes between 1 and the next largest prime squared. I think you still have to proof that a greater primorial also results in larger twin primes.

**10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000**

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**Primenumbers****Member**- Registered: 2013-01-22
- Posts: 141

Thanks googol!

Welcome to the forum!

You're right I don't think it proves anything yet.

**"Time not important. Only life important."*** - The Fifth Element 1997*

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