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**Primenumbers****Member**- Registered: 2013-01-22
- Posts: 128

Triangular numbers are the sum of 1+2+3+4+5+6+7+8..........

a and b= triangular numbers where a>b

Any odd composite= a or (a-b)

This is because the sum of any group of numbers all separated by +1, I.e. 3,4,5,6,7 will be an odd composite with factors of the middle number and the length.

Examples:

2+3+4+5+6+7+8

Middle number=5

Length=7

Therefore=5*7=35

14+15+16+17+18+19+20

Middle number=17

Length=7

Therefore=7*17=119

116+117+118

Middle number=117

Length=3

Therefore=3*117=351

Therefore I would have thought we would be able to compute prime numbers faster by minusing the potential prime, p, off triangular numbers <p to see if they equal another triangular number. If they don't p is prime. This surely must be faster than seeing if p is factorable by all possible factors......................?

Does anyone know how people are using computers to test if very, very, VERY large numbers are prime?

**"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

Hi;

I think they still use the Elliptic curves ECF or Quadratic Sieves.

Take a look here:

https://www.alpertron.com.ar/ECM.HTM

**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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