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## #1 2017-04-20 14:17:37

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

### Triangular numbers and composites

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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## #2 2017-04-20 23:17:58

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

### Re: Triangular numbers and composites

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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