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Old 2020-07-31, 22:13   #12
Alberico Lepore
 
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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[2470649]
b=2092 , a=1/2+sqrt[2470649] , a>1/2*[sqrt[-32*b+4*a^2-4*a+1]+1]>c
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Old 2020-08-01, 07:43   #13
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"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."
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Old 2020-08-01, 18:59   #14
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Quote:
Originally Posted by LaurV View Post
"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."

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
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Old 2020-08-01, 21:26   #15
Batalov
 
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Quote:
Originally Posted by Alberico Lepore View Post
crank == capatost
No,
crank == Disturbo ossessivo-compulsivo (DOC)
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Old 2020-08-02, 01:55   #16
a1call
 
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Quote:
Originally Posted by Batalov View Post
No,
crank == Disturbo ossessivo-compulsivo (DOC)
I hope you were wearing a mustache when you wrote that.
BTW Congrats.

https://youtu.be/hVTUUKCFzvU
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Old 2020-08-02, 05:38   #17
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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 View Post





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
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Old 2020-08-02, 05:40   #18
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We're still waiting to see how you factor 200 digit numbers. That was your claim, prove it.
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Old 2020-08-02, 08:10   #19
Alberico Lepore
 
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Quote:
Originally Posted by Alberico Lepore View Post
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)






P.Š. If it works it can be extended to all a [also to 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
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Old 2020-08-02, 09:05   #20
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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 :+
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Old 2020-08-02, 14:34   #21
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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
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Old 2020-08-03, 09:06   #22
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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
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