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January 2nd, 2017, 12:29 AM   #1
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Factorization . Is this possible ?

prime number * prime number = product

$\displaystyle 2*\sqrt{\frac{1}{3}*product} = N1$

$\displaystyle \sqrt{product} = N2$

$\displaystyle N1 + N2 = N3$

first way $\displaystyle \frac{product}{N3}*3.5 = N4$ --EDIT-- 3.5

second way $\displaystyle \frac{product}{N3}= N4$ --EDIT--

$\displaystyle prime < N4$

$\displaystyle N4$ the distance increases in proportion to the distance of the two factors ,and the distance decreases in proportion to the distance of the two factors. Is this possible ?

Last edited by Aleph6; January 2nd, 2017 at 01:28 AM.
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January 10th, 2017, 10:09 PM   #2
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For example :

$\displaystyle 101 * 3 = 303$

$\displaystyle 2*\sqrt{\frac{1}{3}*303} = 20,...$ $\displaystyle N1$

$\displaystyle \sqrt{303} = 17,...$ $\displaystyle N2$

$\displaystyle 20 + 17 = 37 $ $\displaystyle N3$

first way $\displaystyle \frac{303}{37}*3,5 = 28,... $ $\displaystyle N4$

second way $\displaystyle \frac{303}{37} = 8,...$ $\displaystyle N4$

$\displaystyle 3 < N4$ second way and first way



other example :



$\displaystyle 600000001 * 3 = 1800000003$

$\displaystyle 2*\sqrt{\frac{1}{3}*1800000003} = 48965,...$ $\displaystyle N1$

$\displaystyle \sqrt{1800000003} = 42426,...$ $\displaystyle N2$

$\displaystyle 48965 + 42426 = 91391 $ $\displaystyle N3$

first way $\displaystyle \frac{1800000003}{91391}*3,5 = 68934,... $ $\displaystyle N4$

second way $\displaystyle \frac{1800000003}{91391} = 19695,...$ $\displaystyle N4$

$\displaystyle 3 < N4$ second way and first way


other example :




$\displaystyle 211*101 = 21311$

$\displaystyle 2*\sqrt{\frac{1}{3}*21311} = 168,...$ $\displaystyle N1$

$\displaystyle \sqrt{21311} = 145,...$ $\displaystyle N2$

$\displaystyle 168 + 145 = 313 $ $\displaystyle N3$

first way $\displaystyle \frac{21311}{313}*3,5 = 238,... $ $\displaystyle N4$

second way $\displaystyle \frac{21311}{313} = 68,...$ $\displaystyle N4$

$\displaystyle 211 < N4$ only the first way
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January 10th, 2017, 10:16 PM   #3
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Is there a question in here?

Last edited by skipjack; January 11th, 2017 at 06:11 AM.
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January 10th, 2017, 10:34 PM   #4
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Quote:
Originally Posted by romsek View Post
Is there a question in here?
The question is: Can I decrease the factorization time with this formula? or Is there a faster other formula?

Last edited by skipjack; January 11th, 2017 at 06:10 AM.
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