## Rv: [PrimeNumbers] Consecutive Prime Numbers Equation

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• The x Prime[n]  condition is necessary also. ... De: Sebastian Martin Para: Andres Armario ; Ignacio Larosa
Message 1 of 1 , Aug 9, 2008
The x>Prime[n]  condition is necessary also.

De: Sebastian Martin <sebi_sebi@...>
Para: Andres Armario <armario@...>; Ignacio Larosa <ilarrosa@...>; Ignacio Larosa <ilarrosa@...>; Jose Angel Gonzalez <josechu2004@...>; Lista de Matemáticas <matracas@...>; lista de primos <primenumbers@yahoogroups.com>; Phil Carmody <thefatphil@...>; William Bouris <melangebillyb@...>; Yves Gallot <galloty@...>
Asunto: [PrimeNumbers] Consecutive Prime Numbers Equation

Hello all
I  have obtained the following Equation for consecutive prime numbers:

Theorem:

Let:

F[x_,n_]:=LCM[ x-Prime[n] ,x+Prime[ n]]*GCD[x, Product[Prime[ i],{i,1,n} ]]-(x-Prime[ n])*(x+Prime[ n])/2

Let

Sn={x positive integer: F[x,n]=0}

We have

Min Sn=Prime[n+1]

Sincerely

Sebastián Martín Ruiz

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