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Old 2020-12-29, 04:26   #1
ONeil
 
Dec 2017

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Minus I (have not) found factors for 2^109947391-1, I shot myself in the foot!

Although I really wanted to find a Mersenne Prime number with 2^109947391-1, the facts are facts and it has factors other than 1 and itself. I spent a couple of weeks messing around with Pythonic code tweaking it to see if I could reveal factors. Well 2^109947391-1 starts its factors low with the number 13 and produces a monster cofactor, the cofactor I cannot put in the spoiler, because its to large. I will also kindly leave the code which helped me find the factors. I think I somehow have broke cryptography to a certain degree by finding a factor and having prior knowledge for a giant number other than the kind folks here at GIMPS!

Here at this site you can see I'm running an LL on the the exponent 2^109947391-1, but now I find it kind of fruitless.
https://www.mersenne.org/report_expo...ll=1&ecmhist=1

You can use this site to divide or multiply numbers with high precision to see that I'm correct about finding the factor for 2^109947391-1.
http://www.javascripter.net/math/cal...calculator.htm

Or if your good at python than I provide the factor for the most talked about exponent of 2020-21:

Now if you wish to factor your own number quickly it can be done, however you need to download mprint and print the number you wish to factor with the code I will provide. Here is the site for mprint:
http://www.apfloat.org/apfloat/




First here is the hidden factor: The code is next:

13

The code which found the factor WHICH beat GIMPS!

Code:
#!/usr/local/bin/python
# -*- coding: utf-8 -*-
import math
import time
import random 
import sys

#y^2=x^3+ax+b mod n 
prime=[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271 ]
# ax+by=gcd(a,b). This function returns [gcd(a,b),x,y]. Source Wikipedia
def extended_gcd(a,b):   
	x,y,lastx,lasty=0,1,1,0
	while b!=0:
		q=a/b
		a,b=b,a%b
		x,lastx=(lastx-q*x,x)
		y,lasty=(lasty-q*y,y)
	if a<0: 
		return (-a,-lastx,-lasty)
	else:
		return (a,lastx,lasty)
# pick first a point P=(u,v) with random non-zero coordinates u,v (mod N), then pick a random non-zero A (mod N), 
# then take B = u^2 - v^3 - Ax (mod N).
# http://en.wikipedia.org/wiki/Lenstra_elliptic_curve_factorization
def randomCurve(N):
	A,u,v=random.randrange(N),random.randrange(N),random.randrange(N)
	B=(v*v-u*u*u-A*u)%N
	return [(A,B,N),(u,v)]
	# Given the curve y^2 = x^3 + ax + b over the field K (whose characteristic we assume to be neither 2 nor 3), and points
	# P = (xP, yP) and Q = (xQ, yQ) on the curve, assume first that xP != xQ. Let the slope of the line s = (yP - yQ)/(xP - xQ); since K 	       # is a field, s is well-defined. Then we can define R = P + Q = (xR, - yR) by
	#	s=(xP-xQ)/(yP-yQ) Mod N		
	#	xR=s^2-xP-xQ	Mod N
	#	yR=yP+s(xR-xP)	Mod N 
	# If xP = xQ, then there are two options: if yP = -yQ, including the case where yP = yQ = 0, then the sum is defined as 0[Identity]. 	       # thus, the inverse of each point on the curve is found by reflecting it across the x-axis. If yP = yQ != 0, then R = P + P = 2P = 	      # (xR, -yR) is given by
	#	s=3xP^2+a/(2yP)	Mod N	
	#	xR=s^2-2xP	Mod N
	#	yR=yP+s(xR-xP)	Mod N
	#	http://en.wikipedia.org/wiki/Elliptic_curve#The_group_law''')
	
def addPoint(E,p_1,p_2):
	if p_1=="Identity": return [p_2,1]
	if p_2=="Identity": return [p_1,1]
	a,b,n=E
	(x_1,y_1)=p_1
	(x_2,y_2)=p_2
	x_1%=n
	y_1%=n
	x_2%=n
	y_2%=n
	if x_1 != x_2 :
		d,u,v=extended_gcd(x_1-x_2,n)
		s=((y_1-y_2)*u)%n
		x_3=(s*s-x_1-x_2)%n
		y_3=(-y_1-s*(x_3-x_1))%n
	else:
		if (y_1+y_2)%n==0:return ["Identity",1]
		else:
			d,u,v=extended_gcd(2*y_1,n)
			s=((3*x_1*x_1+a)*u)%n
			x_3=(s*s-2*x_1)%n
			y_3=(-y_1-s*(x_3-x_1))%n
	return [(x_3,y_3),d]
	# http://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication
	#	Q=0 [Identity element]
	#	while m:
	#		if (m is odd) Q+=P
	#		P+=P
	#		m/=2
	#	return Q')
def mulPoint(E,P,m):
	Ret="Identity"
	d=1
	while m!=0:
		if m%2!=0: Ret,d=addPoint(E,Ret,P)
		if d!=1 : return [Ret,d]  # as soon as i got anything otherthan 1 return 
		P,d=addPoint(E,P,P)
		if d!=1 : return [Ret,d]
		m>>=1
	return [Ret,d]
def ellipticFactor(N,m,times=5):
	for i in range(times):
		E,P=randomCurve(N);
		Q,d=mulPoint(E,P,m)
		if d!=1 : return d
	return N
first=True

# ENTER YOUR NUMBER TO FACTOR FOR n:
n = 2047
#	n =
if (len(sys.argv)>1):
		n=int(sys.argv[1])
#	print (n,'=',)

for p in prime:
	while n%p==0:
		if (first==True):
			print (p,)

			break
			first=False
		else:
			print ('x',p,)
			break
		n/=p
m=int(math.factorial(2000))
while n!=1:
	k=ellipticFactor(n,m)
	n//=k
	if (first==True):
		print (k,)
		first=False
#		else:
		print ('x',k,)
		break

Last fiddled with by ONeil on 2020-12-29 at 04:55
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Old 2020-12-29, 04:43   #2
CRGreathouse
 
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Quote:
Originally Posted by ONeil View Post
Although I really wanted to find a Mersenne Prime number with 2^109947391-1, the facts are facts and it has factors other than 1 and itself. I spent a couple of weeks messing around with Pythonic code tweaking it to see if I could reveal factors. Well 2^109947391-1 starts its factors low with the number 13 and produces a monster cofactor, the cofactor I cannot put in the spoiler, because its to large.
Code:
> Mod(2,13)^109947391-1
%1 = Mod(10, 13)
Sorry, try again next time. You might want to read up on the special form of Mersenne divisors.
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Old 2020-12-29, 04:47   #3
retina
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Quote:
Originally Posted by ONeil View Post
The code which found the factor WHICH beat GIMPS!
Beat GIMPS at what? Producing bogus results? Because that is what you have done.
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Old 2020-12-29, 05:03   #4
ONeil
 
Dec 2017

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Quote:
Originally Posted by CRGreathouse View Post
Code:
> Mod(2,13)^109947391-1
%1 = Mod(10, 13)
Sorry, try again next time. You might want to read up on the special form of Mersenne divisors.


Why when I multiply 13 after I divide it by 13 the result = 2^109947391-1 so what you are saying is I should go the full distance on the Lucas Lemer test and their is still hope. This is strange I have not stopped the processing the number yet.
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Old 2020-12-29, 05:09   #5
retina
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Since you love Python so much, try this:
Code:
print((2 ** 109947391 - 1) % 13)
If it is a divisor then it should display 0, like this:
Code:
print((2 ** 11 - 1) % 23)

Last fiddled with by retina on 2020-12-29 at 05:10
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Old 2020-12-29, 05:48   #6
ONeil
 
Dec 2017

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Quote:
Originally Posted by retina View Post
Since you love Python so much, try this:
Code:
print((2 ** 109947391 - 1) % 13)
If it is a divisor then it should display 0, like this:
Code:
print((2 ** 11 - 1) % 23)

I have proof and I'm posting the video. First off you need to use mprint to print out the entire number then like this:

n = hugeexponent % 13

print(n)

n=0

video will be posted ok!
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Old 2020-12-29, 05:53   #7
VBCurtis
 
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You're so bad at math you don't even understand why you're wrong when told you're wrong.

No Mersenne-form number 2^p-1 can have a factor smaller than p. It's not possible. This is easily proved, easily enough that you ought to be able to understand the proof if you go read it.

In fact, no factor smaller than 2p+1 is possible.

That's why it is obvious even to non-coders that your code is garbage. Your ignorance and trolling are tiring.
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Old 2020-12-29, 06:01   #8
ONeil
 
Dec 2017

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Quote:
Originally Posted by VBCurtis View Post
You're so bad at math you don't even understand why you're wrong when told you're wrong.

No Mersenne-form number 2^p-1 can have a factor smaller than p. It's not possible. This is easily proved, easily enough that you ought to be able to understand the proof if you go read it.

In fact, no factor smaller than 2p+1 is possible.

That's why it is obvious even to non-coders that your code is garbage. Your ignorance and trolling are tiring.
Maybe there is an exception when I mod 13 the huge number its ZERO!!!!!!!!!
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Old 2020-12-29, 06:09   #9
ONeil
 
Dec 2017

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Here is the video proof that when you mod the exponent by 13 its zero. period:

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Old 2020-12-29, 06:22   #10
Uncwilly
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I went to the site that you used.
http://javascripter.net/math/calcula...calculator.htm
I entered 2 in the X field and 109947391 in the Y field, then hit the X^Y button and got:
This computation would take too long as the answer. Most likely your input was truncated.
Try again.
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Old 2020-12-29, 06:25   #11
ONeil
 
Dec 2017

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Quote:
Originally Posted by Uncwilly View Post
I went to the site that you used.
http://javascripter.net/math/calcula...calculator.htm
I entered 2 in the X field and 109947391 in the Y field, then hit the X^Y button and got:
This computation would take too long as the answer. Most likely your input was truncated.
Try again.
Wrong I did not use that formula face it guys your beat now go back to your crypto graves along with your cubicles and quit editing my titles your a bunch of weirdos I cracked RSA face it.
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