 mersenneforum.org Mersenne factorization by (nxy+x+y)
 Register FAQ Search Today's Posts Mark Forums Read 2020-08-20, 20:47 #1 baih   Jun 2019 2·17 Posts Mersenne factorization by (nxy+x+y) Let Mersenne number 2n -1 if 2n -1 composite 2n -1 = n2xy + (x+y)n + 1 so 2n /n = (n2xy + (x+y)n) /n = nxy+x+y Finding the x and y we can factor the number into a product (nx)+1 and (ny)+1 example 211-1 = 2047 (2047-1) /2= 186 186 = nxy+x+y = 11* 8*2 + 8+2 X= 8 Y=2 and 2047 = (88+1)*(22+1) Difficulty and complexity (nxy+x+y) like a Diophantine equation Are there any solutions? sory for my english   2020-08-20, 22:20 #2 Viliam Furik   "Viliam Furík" Jul 2018 Martin, Slovakia 653 Posts Obvious mistakes I would like to point out a few mistakes. 1. (2^n) is never divisible by (n), (2^n-2) is divisible by (n), when (n) is prime (btw, it is because of Little Fermat theorem) 2. (2047-1) /2= 186; you probably meant (2047-1)/11 = 186. Apart from these typos, I guess I will leave the topic for other guys.   2020-08-20, 22:27   #3
baih

Jun 2019

2×17 Posts Quote:
 Originally Posted by Viliam Furik I would like to point out a few mistakes. 1. (2^n) is never divisible by (n), (2^n-2) is divisible by (n), when (n) is prime (btw, it is because of Little Fermat theorem) 2. (2047-1) /2= 186; you probably meant (2047-1)/11 = 186. Apart from these typos, I guess I will leave the topic for other guys.
thanks i mean (2^n)-2

Last fiddled with by baih on 2020-08-20 at 22:29   2020-08-21, 00:38 #4 Batalov   "Serge" Mar 2008 Phi(4,2^7658614+1)/2 13×733 Posts Please demonstrate the power of this method on a tiny number 2^1277-1. it is composite. Show us.   2020-08-21, 01:09   #5
baih

Jun 2019

2×17 Posts Quote:
 Originally Posted by Batalov Please demonstrate the power of this method on a tiny number 2^1277-1. it is composite. Show us.
non

The difficulty is the same as the difficulty of (Trial division)
But it may help in some cases

If someone found a solution to the equation c=nxy+x+y

Last fiddled with by baih on 2020-08-21 at 01:17   2020-08-21, 03:21   #6
mathwiz

Mar 2019

22×72 Posts Quote:
 Originally Posted by baih If someone found a solution to the equation c=nxy+x+y
There's infinitely many solutions: c=x=y=0, x=y=1 and c=n+2, and so on.

What is the purpose of this is equation and what constraints are you placing on the variables?   2020-08-21, 03:42   #7
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

3×5×139 Posts Quote:
 Originally Posted by baih Let Mersenne number 2n -1 if 2n -1 composite 2n -1 = n2xy + (x+y)n + 1 so 2n /n = (n2xy + (x+y)n) /n = nxy+x+y Finding the x and y we can factor the number into a product (nx)+1 and (ny)+1 example 211-1 = 2047 (2047-1) /2= 186 186 = nxy+x+y = 11* 8*2 + 8+2 X= 8 Y=2 and 2047 = (88+1)*(22+1) Difficulty and complexity (nxy+x+y) like a Diophantine equation Are there any solutions? sory for my english
That's a good find. I think I have a similar post here somewhere.

The problem is you need brute-force (trying different integers for a solution) and the combinations are astronomically large.

You might have some fun with Wolfram-Alpha:

https://www.wolframalpha.com/input/?...er+the+integer

https://www.wolframalpha.com/input/?...er+the+integer

Good luck, try expanding the concept. You might get something interesting or at worst expand your thinking-power in the process.   2020-08-25, 07:55   #8
LaurV
Romulan Interpreter

Jun 2011
Thailand

3·3,251 Posts Quote:
 Originally Posted by a1call I think I have a similar post here somewhere.
Except your post was left-aligned, therefore easier to read, haha. This is just some rubbish thrown in the middle of the screen, impossible to read.  Thread Tools Show Printable Version Email this Page Similar Threads Thread Thread Starter Forum Replies Last Post Alberico Lepore Alberico Lepore 1 2020-05-27 12:20 thorken Software 53 2019-01-29 15:34 thorken Software 66 2019-01-13 21:08 science_man_88 Miscellaneous Math 3 2010-10-13 14:32 optim PrimeNet 13 2004-07-09 13:51

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