Re: prime factors shortcut question

  • From: "black ares" <matematicianu2003@xxxxxxxxxxx>
  • To: <programmingblind@xxxxxxxxxxxxx>
  • Date: Sat, 10 Oct 2009 08:24:54 +0300

in fact you take the number 22
you will take the square root it is 4.
you search amoung all primes less than square root until you find one which divides your number. 
In our case you find 2.
You divide your number by that prime found and for the result you repeat the algorithm You repeat this algorithm until you will not find any prime less than the square root which divides your number. In our case 22/2=11 square root of 11 is 3 the only prime less than 3 is 2 you take the modulo of 11 to 2 and you find that is 1 not 0 so stop. Now the last number you found is also a prime factor so the result of your program is 2, 11. 
In a pseudo language I see tthe code like this:

int num=22;//any other number works
bool ready=false;
arraylist results=new arraylist();
while(!ready)
{
if(num%2==0)
{
results.add(2);
num/=2;
continue;
}
int sq=Math.Floor(Math.Sqrt(num));
int i=3;
for(i=3; i<=sq; i+=2)
{
if(num%i==0)
{
num/=i;
results.add(i);
break;
}

}
if(i>sq)
{
ready=true;
results.add(num);
}
}
----- Original Message ----- From: "qubit" <lauraeaves@xxxxxxxxx> 
To: <programmingblind@xxxxxxxxxxxxx>
Sent: Saturday, October 10, 2009 7:41 AM
Subject: Re: prime factors shortcut question



no, you are not understanding what I'm saying...
Do the following:

maxfac = floor(sqrt(22))

This yields 4, as you said.

Now walk through all the primes p greater than 1 and less than or equal to
maxfac.  The only prime is 2, as you said.
But 22 divided by 2 is 11, which is prime.  So it can be added to the pool
of primes.  Therefore you already know that 11 is prime without actually
doint the math for all the numbers instead of those less than 4.
The algorithm is something like the following pseudo code:

// num = number being factored
max = floor(square root of num)
for each prime between 2 and floor(square root(num)
Doing it any more would give duplicate results.

Anyway, sorry about the inconvenience. Happy reading.
--le
----- Original Message ----- From: "Alex Hall" <mehgcap@xxxxxxxxx> 
To: <programmingblind@xxxxxxxxxxxxx>
Sent: Friday, October 09, 2009 10:56 PM
Subject: Re: prime factors shortcut question
I will try it. A question, though: is this only for certain numbers? Look at 
22 (2*11):
Math.floor(sqrt(22))=4
factors of 4: 2
no 11?


Have a great day,
Alex
New email address: mehgcap@xxxxxxxxx
----- Original Message ----- From: "qubit" <lauraeaves@xxxxxxxxx> 
To: <programmingblind@xxxxxxxxxxxxx>
Sent: Friday, October 09, 2009 11:41 PM
Subject: Re: prime factors shortcut question



take the floor of the square root. --le
----- Original Message ----- From: "Alex Hall" <mehgcap@xxxxxxxxx> 
To: "Blind Programming List" <programmingblind@xxxxxxxxxxxxx>
Sent: Friday, October 09, 2009 2:13 PM
Subject: prime factors shortcut question


Hi all,
I am trying to find the prime factors of a massive number, over 600
billion,
in perl (it is just an activity in a class, not an assignment). I know you 
can factor the square root, which is good since I cannot store such a big
number in a simple scalar in perl, but I run into a problem: the square
root
of my number is not a whole number, but a decimal. Of course, then, any
modulus I try will not work since a decimal mod any whole number will not
return 0. What do I do? Do I get the floor or ceiling of the square root
operation? Is there another trick? I do not need something vastly complex
that works for most situations or explains things from a cryptographic
standpoint, all I need is what to do with my decimal square root so
modding
works and gives me factors. Thanks for any help!


Have a great day,
Alex
New email address: mehgcap@xxxxxxxxx

__________
View the list's information and change your settings at
//www.freelists.org/list/programmingblind

__________
View the list's information and change your settings at
//www.freelists.org/list/programmingblind



__________
View the list's information and change your settings at
//www.freelists.org/list/programmingblind

__________
View the list's information and change your settings at
//www.freelists.org/list/programmingblind



__________
View the list's information and change your settings at //www.freelists.org/list/programmingblind

Other related posts:

  1. Home
  2. programmingblind
  3. Archive
  4. 10-2009