mersenneforum.org the sound of silence
 Register FAQ Search Today's Posts Mark Forums Read

 2020-11-07, 14:19 #1 Alberico Lepore     May 2017 ITALY 7338 Posts the sound of silence hey @CRGreathouse here is your log y if N=p*q & p+q-4 mod 8 = 0 & (q-p+2)/4=y is odd [but ...] M=(3*N-1)/8 special formula Z=(2*M-3*y+1)/24 Example N=507 3*(((2*190-3*y+1)/24)+3*x*(x+1)/2)+1=A , sqrt(y^2)=2*sqrt(a^2)+1 , 3*(((2*A-3*a+1)/24)+3*x*(x+1)/2)+1=B , sqrt(a^2)=2*sqrt(b^2)+1 , 3*(((2*B-3*b+1)/24)+3*x*(x+1)/2)+1=12*x*(x+1)/2+1 , b=1 || b=-1 q=2*(3*x+1-(x-y+1))+1 https://www.youtube.com/watch?v=8FB9GYkIT3E
2020-11-07, 14:59   #2
Alberico Lepore

May 2017
ITALY

7338 Posts

Quote:
 Originally Posted by Alberico Lepore hey @CRGreathouse here is your log y if N=p*q & p+q-4 mod 8 = 0 & (q-p+2)/4=y is odd [but ...] M=(3*N-1)/8 special formula Z=(2*M-3*y+1)/24 Example N=507 3*(((2*190-3*y+1)/24)+3*x*(x+1)/2)+1=A , sqrt(y^2)=2*sqrt(a^2)+-1 , 3*(((2*A-3*a+1)/24)+3*x*(x+1)/2)+1=B , sqrt(a^2)=2*sqrt(b^2)+-1 , 3*(((2*B-3*b+1)/24)+3*x*(x+1)/2)+1=12*x*(x+1)/2+1 , b=1 || b=-1 q=2*(3*x+1-(x-y+1))+1 https://www.youtube.com/watch?v=8FB9GYkIT3E
there is a small mistake that makes it all in vain

red - correction

 2020-11-08, 06:00 #3 Alberico Lepore     May 2017 ITALY 52×19 Posts I fixed the bug it should now be correct Example N=507 3*(((2*190-3*y+1)/24)+3*x*(x+1)/2)+1=A , sqrt(y^2)=sqrt((2*a-1)^2) , 3*(((2*A-3*a+1)/24)+3*x*(x+1)/2)+1=B , sqrt(a^2)=sqrt((2*b-1)^2) , 3*(((2*B-3*b+1)/24)+3*x*(x+1)/2)+1=12*x*(x+1)/2+1 , b=1 || b=-1 Example N=595 3*(((2*223-3*y+1)/24)+3*x*(x+1)/2)+1=A , sqrt(y^2)=sqrt((2*a-1)^2) , 3*(((2*A-3*a+1)/24)+3*x*(x+1)/2)+1=B , sqrt(a^2)=sqrt((2*b-1)^2) , 3*(((2*B-3*b+1)/24)+3*x*(x+1)/2)+1=12*x*(x+1)/2+1 , b=1 || b=-1
 2020-11-08, 15:49 #4 Alberico Lepore     May 2017 ITALY 52·19 Posts if I am not wrong this is the demonstration ((2*(3*N-1)/8-3*y+1)/24)=x*(x+1)/2-(y+1)/2*(y-1)/2/2 , p*q=N , q=2*(3*x+1-(x-y+1))+1 , p=2*(3*x+1-(x-y+1))+1-(4*y-2) , p*q=N=(8*M+1)/3 , (p-2)*(q+2)=(8*(M-3*y)+1)/3 , (2*M-3*y+1)=(2*(M-3*y)+3*y+1) , 3*(((2*(3*N-1)/8-3*y+1)/24)+3*x*(x+1)/2)+1=12*x*(x+1)/2+1-3*(y+1)/2*(y-1)/2/2 please feedback Last fiddled with by Alberico Lepore on 2020-11-09 at 05:51
 2020-11-11, 11:08 #5 Alberico Lepore     May 2017 ITALY 52×19 Posts then not to test at any level of log y log y must be overcome example 3*(((2*250-3*(1-y)+1)/24)+3*x*(x+1)/2)+1=A , sqrt((1-y)^2)=sqrt((2*a-1)^2) , 3*(((2*A-3*a+1)/24)+3*x*(x+1)/2)+1=B , sqrt(a^2)=sqrt((2*b-1)^2) , 3*(((2*B-3*b+1)/24)+3*x*(x+1)/2)+1=B , b=1 in the example i used 250 which has an even y
 2020-11-11, 15:26 #6 Alberico Lepore     May 2017 ITALY 52·19 Posts another type of implementation based on the same principle is this [if I have not made mistakes] 3*(((2*190-3*y+1)/24)+3*x*(x+1)/2)+1=A , y=2*[(-1)^((y+1)/2-1)]*a+(-1)^[(-1)^((y+1)/2)] , 3*(((2*A-3*a+1)/24)+3*x*(x+1)/2)+1=B , [(-1)^((y+1)/2-1)]*a=2*[(-1)^[[[(-1)^((y+1)/2-1)]*a+1]/2-1]]*b+(-1)^[(-1)^[[[(-1)^((y+1)/2-1)]*a+1]/2]] , 3*(((2*B-3*b+1)/24)+3*x*(x+1)/2)+1=C , [(-1)^[[[(-1)^((y+1)/2-1)]*a+1]/2-1]]*b=2*[(-1)^[[[(-1)^[[[(-1)^((y+1)/2-1)]*a+1]/2-1]]*b+1]/2-1]]*c+(-1)^[(-1)^[[[(-1)^[[[(-1)^((y+1)/2-1)]*a+1]/2-1]]*b+1]/2]] , 3*(((2*C-3*c+1)/24)+3*x*(x+1)/2)+1=C , c=1 which of the two is better in your opinion? UPDATE: There are some mistakes tomorrow I will try to update Last fiddled with by Alberico Lepore on 2020-11-11 at 17:16 Reason: UPDATE
 2020-11-12, 09:59 #7 Alberico Lepore     May 2017 ITALY 52×19 Posts this is the best logarithmic implementation I could think of. I leave the implementation to you expert programmers pure logarithm N=507 3*(((2*190-3*y+1)/24)+3*x*(x+1)/2)+1=A , 190=3*x*(x+1)/2-3*y*(y-1)/2+(3*x+1)*(3*x+2)/2 , 3*(((2*A-3*a+1)/24)+3*x*(x+1)/2)+1=B , A+3*a*(a-1)/2=12*x*(x+1)/2+1 , 3*(((2*B-3*b+1)/24)+3*x*(x+1)/2)+1=C , B+3*b*(b-1)/2=12*x*(x+1)/2+1 , 3*(((2*C-3*c+1)/24)+3*x*(x+1)/2)+1=C , c=1 ,A,B,C,x,y>0 Last fiddled with by Alberico Lepore on 2020-11-14 at 13:37 Reason: ,A,B,C,x,y>0

 Similar Threads Thread Thread Starter Forum Replies Last Post Cricage Information & Answers 3 2016-01-21 16:49 R.D. Silverman Information & Answers 1 2007-06-26 18:24 Unregistered PrimeNet 7 2006-10-23 15:48 pacionet Software 9 2006-01-22 21:04 JuanTutors Software 8 2004-10-04 06:33

All times are UTC. The time now is 22:03.

Mon Apr 19 22:03:21 UTC 2021 up 11 days, 16:44, 0 users, load averages: 3.06, 3.32, 3.93

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.