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**fireplace****Member**- Registered: 2015-02-07
- Posts: 1

Myself trying find ways to use primes for other purpose than just cryptography.

So what are you guys working on?

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

I am working on finding a solution to proving whether a number is prime or not but at the moment I'm focusing on Goldbach's conjecture which states that any even number can be made up of two primes added together.

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

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Primenumbers wrote:

I am working on finding a solution to proving whether a number is prime or not

Like this?

**LearnMathsFree: Videos on various topics.New: Integration Problem | Adding FractionsPopular: Continued Fractions | Metric Spaces | Duality**

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Working on a better way to determine the coefficients of large expansions. Only requires some research...

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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

zetafunc wrote:

Like this?

More like this;

x is not factorable by 2 or 5.

x = ab

x ends in 1; a and b end in (1,1)(3,7) or (9,9).

x ends in 3; a and b end in (1,3) or (7,9).

x ends in 7; a and b end in (1,7) or (3,9).

x ends in 9; a and b end in (1,9)(3,3) or (7,7).

i.e. 3x9=27.......ends in 7.

by knowing what x ends in we can determine what a and b might end in.

You would have thought knowing what a and b end in you could determine that a number is composite and therefore not prime, turns out it doesn't seem to work that way.

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

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But is that really any better than, say, the Sieve of Eratosthenes?

You would have thought knowing what a and b end in you could determine that a number is composite and therefore not prime, turns out it doesn't seem to work that way.

It wouldn't -- using your notation, x is prime iff (a,b) = (1, x) or (x,1). Even if a or b is 1 modulo 10, that doesn't guarantee that a or b is 1, and for large x, will give you a very large number of possibilities.

**LearnMathsFree: Videos on various topics.New: Integration Problem | Adding FractionsPopular: Continued Fractions | Metric Spaces | Duality**

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

zetafunc wrote:

Even if a or b is 1 modulo 10, that doesn't guarantee that a or b is 1, and for large x, will give you a very large number of possibilities.

If x = (10c + d)(10e + f) where d and f = 1,3,7 or 9 I just have to prove c and e > 0 granted that x is not factorable by 2,5,3,7. i.e. a and b > 10.

I know how to prove x is not factorable by 2,3,5 or 7, I don't know how to prove that c and e are both >0.

But say I knew what d and f were, you would have thought I'd be able to work out what c and e were................ Don't you think?

*Last edited by Primenumbers (2015-06-17 22:46:30)*

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

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

**Rule for primes;**

x! is factorable by x only once when x is prime and more than once when x is not prime. This only happens when x>4.

If x=ab, ab occurs more than once, i.e. x!=axbxabx?

If x=

, occurs more than once i.e. x!=ax2ax. Unless =2 or less and x= 4 or1. a>2 is fine.I think this is simpler than x/x! factors down when x is not prime and doesn't when x is prime!

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

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

zetafunc wrote:

But is that really any better than, say, the Sieve of Eratosthenes?

You would have thought knowing what a and b end in you could determine that a number is composite and therefore not prime, turns out it doesn't seem to work that way.

It wouldn't -- using your notation, x is prime iff (a,b) = (1, x) or (x,1). Even if a or b is 1 modulo 10, that doesn't guarantee that a or b is 1, and for large x, will give you a very large number of possibilities.

I still don't get this post..................? Is 1 modulo 10 a mathematical way of saying, ends in 1.....? I was trying to prove x is composite not prime......? a or b ending in 1 wouldn't guarantee x is prime...?

*Last edited by Primenumbers (2015-06-23 10:28:57)*

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

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

That is what

Even if a or b is 1 modulo 10

means. And of course zetafunc is correct ending in a 1 does not guarantee primality.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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

Ok, cool.

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

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