 mersenneforum.org Procedure for factorizing N into O (1) ...Not.
 Register FAQ Search Today's Posts Mark Forums Read  2020-07-31, 22:13 #12 Alberico Lepore   May 2017 ITALY 19416 Posts This is a certainty solve (-36*1^3+117*1^2-((M+3)*36+20+36*(c-1)*c/2)*1+(M*60+55)+60*(c-1)*c/2)/2-4>24*(b-1)*(b-1+1) , (4*b+2)^2-(2*a-1)^2=((M*3+1)*8+1)/3 , b,M -> b>1/8*(a^2-a-c^2+c) -> a<1/2*[sqrt[32*b+4*c^2-4*c+1]+1] -> c>1/2*[sqrt[-32*b+4*a^2-4*a+1]+1] -> a > c > 1/2*[sqrt[-32*b+4*a^2-4*a+1]+1] instead the following is a draft that I will deepen in the coming days Examples O(log) Example 1 N=451 -> M=56 case c < 1/2*[sqrt[32*b+4*a^2-4*a+1]+1] < a (-36*1^3+117*1^2-(59*36+20+36*(c-1)*c/2)*1+(56*60+55)+60*(c-1)*c/2)/2-4>24*(b-1)*(b-1+1) , c=2 -> b < 5.86.. -> b=5 -> b=5 , (4*b+2)^2-(2*a-1)^2=((56*3+1)*8+1)/3 -> a=1/2+sqrt(33)/2 -> b=5 , a=1/2+sqrt(33)/2 , 1/2*[sqrt[-32*b+4*a^2-4*a+1]+1] = complex number (irrational) case c > a (-36*1^3+117*1^2-(59*36+20+36*(c-1)*c/2)*1+(56*60+55)+60*(c-1)*c/2)/2-4>24*(b-1)*(b-1+1) , c=9 -> b < 7.30... -> b=7 -> b=7 , (4*b+2)^2-(2*a-1)^2=((56*3+1)*8+1)/3 -> a=1/2+sqrt(449)/2 -> b=7 , a=1/2+sqrt(449)/2 , a>c>1/2*[sqrt[-32*b+4*a^2-4*a+1]+1] Example 2 N=67586227 -> M=8448281 case c < 1/2*[sqrt[32*b+4*a^2-4*a+1]+1] < a (-36*1^3+117*1^2-(8448281*36+20+36*(c-1)*c/2)*1+(8448278*60+55)+60*(c-1)*c/2)/2-4>24*(b-1)*(b-1+1) , c=786 -> b<2092.96 -> b=2092 b=2092 ,(4*b+2)^2-(2*a-1)^2=((8448281*3+1)*8+1)/3 -> a=1/2+sqrt b=2092 , a=1/2+sqrt , a>1/2*[sqrt[-32*b+4*a^2-4*a+1]+1]>c   2020-08-01, 07:43 #13 LaurV Romulan Interpreter   Jun 2011 Thailand 863510 Posts "A crank is a person inexplicably obsessed by an obviously unsound idea—a person with a bee in his bonnet. To call a person a crank is to say that because of some quirk of temperament he is wasting his time pursuing a line of thought that is plainly without merit or promise ... To call a person a crank is basically just a colorful and insulting way of expressing disagreement with his master idea, and it therefore belongs to the language of controversy rather than to the language of defamation." Judge Richard Posner.   2020-08-01, 18:59   #14
Alberico Lepore

May 2017
ITALY

22×101 Posts Quote:
 Originally Posted by LaurV "A crank is a person inexplicably obsessed by an obviously unsound idea—a person with a bee in his bonnet. To call a person a crank is to say that because of some quirk of temperament he is wasting his time pursuing a line of thought that is plainly without merit or promise ... To call a person a crank is basically just a colorful and insulting way of expressing disagreement with his master idea, and it therefore belongs to the language of controversy rather than to the language of defamation." Judge Richard Posner.

crank == capatost

Code:
b=5
18*(121*(121-1)+120)=A ,18*(a*(a-1)+120)=B , a=1 , A=263520 B=2160 C=1830  D=610 E=20
18*(119*(119-1)+118)=A ,18*(a*(a-1)+118)=B , a=2 , A=254880 B=2160 C=1770  D=590 E=39
18*(115*(115-1)+114)=A ,18*(a*(a-1)+114)=B , a=3 , A=238032 B=2160 C=1653  D=551 E=56
18*(109*(109-1)+108)=A ,18*(a*(a-1)+108)=B , a=4 , A=213840 B=2160 C=1485  D=495 E=70
18*(101*(101-1)+100)=A ,18*(a*(a-1)+100)=B , a=5 , A=183600 B=2160 C=1275  D=425 E=80
18*(91*(91-1)+90)=A ,18*(a*(a-1)+90)=B     , a=6 , A=149040 B=2160 C=1035  D=345 E=85
18*(79*(79-1)+78)=A ,18*(a*(a-1)+78)=B     , a=7 , A=112320 B=2160 C=780   D=260 E=84
18*(65*(65-1)+64)=A ,18*(a*(a-1)+64)=B     , a=8 , A=76032  B=2160 C=528   D=176

b=6
18*(169*(169-1)+168)=A ,18*(a*(a-1)+168)=B , a=1 , A=514080 B=3024 C=3570  D=1190 E=28
18*(167*(167-1)+166)=A ,18*(a*(a-1)+166)=B , a=2 , A=501984 B=3024 C=3486  D=1162 E=55
18*(163*(163-1)+162)=A ,18*(a*(a-1)+162)=B , a=3 , A=478224 B=3024 C=3321  D=1107 E=80
18*(157*(157-1)+156)=A ,18*(a*(a-1)+156)=B , a=4 , A=443664 B=3024 C=3081  D=1027 E=102
18*(149*(149-1)+148)=A ,18*(a*(a-1)+148)=B , a=5 , A=399600 B=3024 C=2775  D=925  E=120
18*(139*(139-1)+138)=A ,18*(a*(a-1)+138)=B , a=6 , A=347760 B=3024 C=2415  D=805  E=133
18*(127*(127-1)+126)=A ,18*(a*(a-1)+126)=B , a=7 , A=290304 B=3024 C=2016  D=672  E=140
18*(113*(113-1)+112)=A ,18*(a*(a-1)+112)=B , a=8 , A=229824 B=3024 C=1596  D=532  E=140
18*(97*(97-1)+96)=A ,18*(a*(a-1)+96)=B     , a=9 , A=169344 B=3024 C=1176  D=392

805-2*18*((139-2*a)*((139-2*a)-1)+(138-2*a))/432+18*((139-4*a-2)*((139-4*a-2)-1)+(138-4*a-2))/432=A

805-2*18*((139-2*a)*((139-2*a)-1)+(138-2*a))/432+18*((139-4*a-2)*((139-4*a-2)-1)+(138-4*a-2))/432=-a-1   2020-08-01, 21:26   #15
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

215708 Posts Quote:
 Originally Posted by Alberico Lepore crank == capatost
No,
crank == Disturbo ossessivo-compulsivo (DOC)   2020-08-02, 01:55   #16
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

73E16 Posts Quote:
 Originally Posted by Batalov No, crank == Disturbo ossessivo-compulsivo (DOC)
I hope you were wearing a mustache when you wrote that. BTW Congrats.

https://youtu.be/hVTUUKCFzvU   2020-08-02, 05:38   #17
Alberico Lepore

May 2017
ITALY

22×101 Posts Apart from jokes what do you think?

Let N=(4*b+2)^2-(2*a-1)^2=p*q -> p=(4*b+2-(2*a-1)) and q=(4*b+2+(2*a-1)) ->p+q=8*b+4 -> q-p=4*a-2

Let H=2*((3*N-1)/8-1)/3+1 ed a<b [a=b+1 , N=3*p*q with p=q]

then

18*(H*(H-1)+H-1)/432-2*18*((H-2*a)*((H-2*a)-1)+(H-1-2*a))/432+18*((H-4*a-2)*((H-4*a-2)-1)+(H-1-4*a-2))/432=-a-1

How to read the legend below:

18*(H*(H-1)+H-1)=A ,18*(a*(a-1)+H-1)=B , a=a , A=A B=B C=A/144 D=C/3 E=D(a)-D(a+1)

Quote:
 Originally Posted by Alberico Lepore Code: b=6 18*(121*(121-1)+120)=A ,18*(a*(a-1)+120)=B , a=1 , A=263520 B=2160 C=1830 D=610 E=20 18*(119*(119-1)+118)=A ,18*(a*(a-1)+118)=B , a=2 , A=254880 B=2160 C=1770 D=590 E=39 18*(115*(115-1)+114)=A ,18*(a*(a-1)+114)=B , a=3 , A=238032 B=2160 C=1653 D=551 E=56 18*(109*(109-1)+108)=A ,18*(a*(a-1)+108)=B , a=4 , A=213840 B=2160 C=1485 D=495 E=70 18*(101*(101-1)+100)=A ,18*(a*(a-1)+100)=B , a=5 , A=183600 B=2160 C=1275 D=425 E=80 18*(91*(91-1)+90)=A ,18*(a*(a-1)+90)=B , a=6 , A=149040 B=2160 C=1035 D=345 E=85 18*(79*(79-1)+78)=A ,18*(a*(a-1)+78)=B , a=7 , A=112320 B=2160 C=780 D=260 E=84 18*(65*(65-1)+64)=A ,18*(a*(a-1)+64)=B , a=8 , A=76032 B=2160 C=528 D=176 b=7 18*(169*(169-1)+168)=A ,18*(a*(a-1)+168)=B , a=1 , A=514080 B=3024 C=3570 D=1190 E=28 18*(167*(167-1)+166)=A ,18*(a*(a-1)+166)=B , a=2 , A=501984 B=3024 C=3486 D=1162 E=55 18*(163*(163-1)+162)=A ,18*(a*(a-1)+162)=B , a=3 , A=478224 B=3024 C=3321 D=1107 E=80 18*(157*(157-1)+156)=A ,18*(a*(a-1)+156)=B , a=4 , A=443664 B=3024 C=3081 D=1027 E=102 18*(149*(149-1)+148)=A ,18*(a*(a-1)+148)=B , a=5 , A=399600 B=3024 C=2775 D=925 E=120 18*(139*(139-1)+138)=A ,18*(a*(a-1)+138)=B , a=6 , A=347760 B=3024 C=2415 D=805 E=133 18*(127*(127-1)+126)=A ,18*(a*(a-1)+126)=B , a=7 , A=290304 B=3024 C=2016 D=672 E=140 18*(113*(113-1)+112)=A ,18*(a*(a-1)+112)=B , a=8 , A=229824 B=3024 C=1596 D=532 E=140 18*(97*(97-1)+96)=A ,18*(a*(a-1)+96)=B , a=9 , A=169344 B=3024 C=1176 D=392 805-2*18*((139-2*a)*((139-2*a)-1)+(138-2*a))/432+18*((139-4*a-2)*((139-4*a-2)-1)+(138-4*a-2))/432=A 805-2*18*((139-2*a)*((139-2*a)-1)+(138-2*a))/432+18*((139-4*a-2)*((139-4*a-2)-1)+(138-4*a-2))/432=-a-1

P.Š. If it works it can be extended to all a [also to a> = b] and to all N

Last fiddled with by Alberico Lepore on 2020-08-02 at 07:55 Reason: [a=b+1 , N=3*p*q with p=q] && 18*(H*(H-1)+H-1)/432 && b=6 b=7   2020-08-02, 05:40 #18 retina Undefined   "The unspeakable one" Jun 2006 My evil lair 10101111100012 Posts We're still waiting to see how you factor 200 digit numbers. That was your claim, prove it.   2020-08-02, 08:10   #19
Alberico Lepore

May 2017
ITALY

22·101 Posts Quote:
 Originally Posted by Alberico Lepore Apart from jokes what do you think? Let N=(4*b+2)^2-(2*a-1)^2=p*q -> p=(4*b+2-(2*a-1)) and q=(4*b+2+(2*a-1)) ->p+q=8*b+4 -> q-p=4*a-2 Let H=2*((3*N-1)/8-1)/3+1 ed a = b] and to all N

unfortunately correct it is

805-2*18*((139-2*a)*((139-2*a)-1)+(138-2*a))/432+18*((139-4*a-2)*((139-4*a-2)-1)+(138-4*a-2))/432=X
,
18*((139+2*(a-1))*((139+2*(a-1))-1)+(138+2*(a-1)))/432-805*2+18*((139-2*a)*((139-2*a)-1)+(138-2*a))/432=Y
,
X-Y=a   2020-08-02, 09:05 #20 Alberico Lepore   May 2017 ITALY 22×101 Posts I share another thing A / B = D / (b * (b-1) / 6) so if b or (b-1) are multiples of 3 and A / B is an integer then b * (b-1) / 6 is an integer dividing D indeed Example N = 627 213840 / [18 * (a * (a-1) +138)] = 495 / [(b * (b-1) / 6)] Now we have to understand when D / (b * (b-1) / 6) is an integer First I would check N = 3 * G EDIT 1 : I share another thing A / B = D / (b * (b-1) / 6)=6*D/( (b * (b-1)) so if A / B is an integer then b * (b-1) is an integer dividing 6*D EDIT 2 : I share another thing A / B = D / (b * (b+1) / 6)=6*D/( (b * (b+1)) so if A / B is an integer then b * (b+1) is an integer dividing 6*D Last fiddled with by Alberico Lepore on 2020-08-02 at 10:41 Reason: EDIT 1 :EDIT 2 :+   2020-08-02, 14:34 #21 Alberico Lepore   May 2017 ITALY 22·101 Posts Reorganizing everything Let N=(4*b+2)^2-(2*a-1)^2=p*q -> p=(4*b+2-(2*a-1)) and q=(4*b+2+(2*a-1)) ->p+q=8*b+4 -> q-p=4*a-2 Let H=2*((3*N-1)/8-1)/3+1 Let 18*(H*(H-1)+H-1)=A ,18*(a*(a-1)+H-1)=B , D=A/432 then A / B = D / (b * (b+1) / 6)=6*D/( (b * (b+1)) so if A / B is an integer then b * (b+1) is an integer dividing 6*D N=187 -> H=47 18*(47*(47-1)+46)=A=39744 ,18*(a*(a-1)+46)=B=864 , a=2 , D=92 92*6/12=39744/864 Analyzing we obtain that the new number to factorize D is at most greater than N of D/N=1/3*(2*b^4+4*b^3+3*b^2+b)/(16*b^2+16*b+3) therefore almost b ^ 2 larger than N So this procedure does not serve to factorize RSA but to bypass its factoring difficulties Indeed observing Se N=(4*b+1)*(4*b+3)=16*b^2+16*b+3 allora H(max)=2*2*b*(b+1)+1 solve H=2*2*b*(b+1)+1 , 18*(H*(H-1)+H-1)/432=D , 6*D/ (b * (b+1))=R -> D=1/3*(2*b^4+4*b^3+3*b^2+b) ; R=4*b^2+4*b+2   2020-08-03, 09:06 #22 Alberico Lepore   May 2017 ITALY 40410 Posts What do you think of this other algorithm that I am writing to you? Let N=(4*b+2)^2-(2*a-1)^2=p*q -> p=(4*b+2-(2*a-1)) and q=(4*b+2+(2*a-1)) ->p+q=8*b+4 -> q-p=4*a-2 Let H=2*((3*N-1)/8-1)/3+1 then 18*(H*(H-1)+H-1)=A ,18*(a*(a-1)+H-1)=B ,6*(a*(a-1)+H-1)=W vary h from 3 to as long as Z is an integer [A-144*1/24*(h-1)*h*(h+1)*(h-2)]=Z GCD(A,Z)=B || W example jump h = 5 because it is our solution 18*(101*(101-1)+100)=A ,18*(a*(a-1)+100)=B -> A=183600 [183600-144*1/24*(h-1)*h*(h+1)*(h-2)]=Z ,h=9 ->153360 GCD(153360,183600)=2160 18*(a*(a-1)+100)=2160 -> a=5 continue with h if we don't find our solution EDIT: RSA difficulties can also be bypassed N=507 solve H=127 , 18*(H*(H-1)+H-1)=A , [A-144*1/24*(a-1)*a*(a+1)*(a-2)]=Z*6*(a*(a-1)+127-1),a,A,H Z^2-508*Z+193540=X^2 Last fiddled with by Alberico Lepore on 2020-08-03 at 12:48 Reason: green edit blue EDIT   Thread Tools Show Printable Version Email this Page Similar Threads Thread Thread Starter Forum Replies Last Post jnml Miscellaneous Math 8 2017-11-01 18:31 Romuald Msieve 24 2015-11-09 20:16 ixfd64 Factoring 4 2012-10-16 04:07 jocelynl Software 3 2004-11-28 12:41 Erasmus PrimeNet 10 2004-02-19 12:09

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