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September 11th, 2017, 06:01 AM   #1
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Goldbach

The formula that generates whole prime numbers :


y=(2^(x-1)-1)/x ( formula-1)

If y is an integer , then x must be absolutely a prime number .
the set of x for any value of integer y ; x = { 3,5,7,11,13,....} and it generates all the prime numbers .

The question is that for the set of prime numbers ( x1 , x2) does the formula generates all the even numbers or not ?
y1 = (2^(x1-1) -1 ) /x1 + (2^(x2-1) -1 ) /x2
for ( x1 , x2) = ( 3,3) then y1 = 2 ;
for ( x1 , x2) = ( 3,5) then y2 = 4 ;
for ( x1 , x2) = ( 5,5) then y3 = 6 ;
for ( x1 , x2) = (5,7) then y4 = 8 ;
....................

The result for whole prime sets of ( x1 , x2) then you can generate all the even number's set .
P.S.: For the proof of formula-1 and to learn more about it please contact me . For example formula-1 must be always divided by 3 .

METE UZUN
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September 11th, 2017, 08:47 AM   #2
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Though $(2^{341-1}-1)/341$ is an integer, 341 = 11 × 31 is composite.
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