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January 2nd, 2017, 12:29 AM  #1 
Newbie Joined: Nov 2016 From: Italia Posts: 5 Thanks: 0  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. 
January 10th, 2017, 10:09 PM  #2 
Newbie Joined: Nov 2016 From: Italia Posts: 5 Thanks: 0  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 
January 10th, 2017, 10:16 PM  #3 
Senior Member Joined: Sep 2015 From: CA Posts: 1,201 Thanks: 613 
Is there a question in here?
Last edited by skipjack; January 11th, 2017 at 06:11 AM. 
January 10th, 2017, 10:34 PM  #4 
Newbie Joined: Nov 2016 From: Italia Posts: 5 Thanks: 0  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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