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November 10th, 2016, 03:31 AM  #1 
Newbie Joined: Nov 2016 From: Italia Posts: 5 Thanks: 0  Find the factor of two primes knowing the product I think I found a kind of formula, what do you say? 3 steps : $\displaystyle p1 * p2 = n$ $\displaystyle \frac{n}{22 * n2}= n3$ (if $\displaystyle n3 = 22,..$ stop) $\displaystyle \frac{n2}{2} = p$ ($\displaystyle n2$ is $\displaystyle p*2$) example : $\displaystyle 997 * 13 = 12961$ $\displaystyle \frac{12961}{22 * 26}= 22,...$ $\displaystyle \frac{26}{2} = 13$ 1st exception : $\displaystyle 32900917867 * 10007 = 329239485095069$ $\displaystyle \frac{329239485095069}{ 22 * 65801835734 } = 227,...$ (22,7...like 22 ) stop $\displaystyle \frac{65801835734}{2} = 32900917867$ 2nd exception : if p = 5 ex.ple 523 $\displaystyle 382631* 523 = 200116013$ $\displaystyle \frac{200116013}{22 *780000} = 11,...$ $\displaystyle \frac{780000}{2} = 390000$ near $\displaystyle p$ because $\displaystyle \frac{200116013}{22 *40000} = 227,...$ $\displaystyle \frac{200116013}{40000}=5002,..$ always $\displaystyle 5...,..$ or very near and correct is this : $\displaystyle \frac{200116013}{22 *780000} = 11,...$ $\displaystyle \frac{780000}{2} = 390000$ near $\displaystyle p$ 
November 10th, 2016, 06:25 AM  #2  
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551  Quote:
I think the problem you have set yourself is this: Find an algorithm that will determine if a positive integer n is the product of exactly two primes, p and q, and, if so, what those two primes are. In other words, n is known, but it is not known whether p and q exist, let alone what they are. So the first step is to compute s and t as follows $s = 2p\ and\ t = \dfrac{n}{22s} = \dfrac{n}{44p}.$ If that is a correct reading, the first step cannot be done because p is unknown and may not even exist. Last edited by JeffM1; November 10th, 2016 at 06:28 AM.  
November 10th, 2016, 10:21 PM  #3  
Newbie Joined: Nov 2016 From: Italia Posts: 5 Thanks: 0  Quote:
$\displaystyle 382631 * 3 = 1147893$ $\displaystyle \frac{1147893}{22 * 230}= 226,8$ $\displaystyle \frac{230}{2}=115$ near $\displaystyle p = 3$ I meant so. Only a product of two primes. Last edited by Aleph6; November 10th, 2016 at 10:44 PM.  
November 11th, 2016, 07:06 AM  #4 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 
I do not mean to seem rude and recognize that English may not be your native language, but I do not understand what you are even trying to do. Please explain exactly what this procedure is supposed to do. As for your example, where does 230 come from, and why is 115 a good approximation to 3? 

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factor, find, knowing, primes, product 
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