mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Miscellaneous Math

Reply
 
Thread Tools
Old 2018-02-26, 18:18   #12
JM Montolio A
 
Feb 2018

25×3 Posts
Default

some "must be" M() values:

( 3: 2) ( 5: 4) ( 7: 3) ( 9: 6)(11:10) (13:12) (15: 4) (17: 8) (19:18)(21: 6) (23:11) (25:20) (27:18) (29:28)

not?
JM Montolio A is offline   Reply With Quote
Old 2018-02-27, 04:09   #13
LaurV
Romulan Interpreter
 
LaurV's Avatar
 
Jun 2011
Thailand

3×2,957 Posts
Default

three observations:

1. the expression "a*b/gcd(a,b)" is usually called "lcm(a,b)", simpler to write...

2. in each of your pairs (x,y) the y is the order of 2 (mod x). In pari/gp, you can get it with the function "znorder". Not more than few days ago, we posted a function in a parallel thread, that computes the same thing, it is called "getp()", look for it.... (it also works for all odd numbers, not necessarily prime).

Code:
gp > znorder(Mod(2,3))
= 2
gp > znorder(Mod(2,5))
= 4
gp > znorder(Mod(2,7))
= 3
gp > znorder(Mod(2,9))
= 6
gp > getp(9)
= 6
gp > getp(25)
= 20
gp >
3. we see where you are going with this, but it will not work. Sooner or later you will run into an obstacle called "wieferich primes" and you will not be able to progress any further. The most of the guys in the world trying to prove this conjecture failed because they never heard of wieferich primes before...

Last fiddled with by LaurV on 2018-02-27 at 04:21
LaurV is offline   Reply With Quote
Old 2018-02-27, 09:52   #14
JM Montolio A
 
Feb 2018

25·3 Posts
Default

oh, functions, thanks

wieferich ... wait ...

¿ Conjecture ? ¿ what conjecture ?
JM Montolio A is offline   Reply With Quote
Old 2018-02-27, 11:50   #15
JM Montolio A
 
Feb 2018

25·3 Posts
Default

M( 1093 ) = 364

M( 3511 ) = 1755
JM Montolio A is offline   Reply With Quote
Old 2018-02-27, 15:36   #16
Dr Sardonicus
 
Dr Sardonicus's Avatar
 
Feb 2017
Nowhere

1101111110002 Posts
Default

Even with your conditions in post #8 and post #11 to this thread [M(p) divides p-1, and if p = 2^e - 1 then M(p) = e], your "function" is only defined unambiguously if either

(1) p is a Mersenne prime, or

(2) 2 is a primitive root (mod p).

Up to the limit 200, the following primes do not satisfy either condition:

For p = 17, the possible values of M(p) are 8 times k for k in [1, 2].
For p = 23, the possible values of M(p) are 11 times k for k in [1, 2].
For p = 41, the possible values of M(p) are 20 times k for k in [1, 2].
For p = 43, the possible values of M(p) are 14 times k for k in [1, 3].
For p = 47, the possible values of M(p) are 23 times k for k in [1, 2].
For p = 71, the possible values of M(p) are 35 times k for k in [1, 2].
For p = 73, the possible values of M(p) are 9 times k for k in [1, 2, 4, 8].
For p = 79, the possible values of M(p) are 39 times k for k in [1, 2].
For p = 89, the possible values of M(p) are 11 times k for k in [1, 2, 4, 8].
For p = 97, the possible values of M(p) are 48 times k for k in [1, 2].
For p = 103, the possible values of M(p) are 51 times k for k in [1, 2].
For p = 109, the possible values of M(p) are 36 times k for k in [1, 3].
For p = 113, the possible values of M(p) are 28 times k for k in [1, 2, 4].
For p = 137, the possible values of M(p) are 68 times k for k in [1, 2].
For p = 151, the possible values of M(p) are 15 times k for k in [1, 2, 5, 10].
For p = 157, the possible values of M(p) are 52 times k for k in [1, 3].
For p = 167, the possible values of M(p) are 83 times k for k in [1, 2].
For p = 191, the possible values of M(p) are 95 times k for k in [1, 2].
For p = 193, the possible values of M(p) are 96 times k for k in [1, 2].
For p = 199, the possible values of M(p) are 99 times k for k in [1, 2].

If you want M(p) to be the multiplicative order of 2 (mod p), please just say so.
Dr Sardonicus is offline   Reply With Quote
Old 2018-02-27, 15:45   #17
JM Montolio A
 
Feb 2018

25×3 Posts
Default

I think the function M() is what user "a3call" names "reverse factoring".

Next post , the method i use on my theories to get M(n).

But i suspect the method used for a3call is much better.

Sorry ¿ some place to share a windows64.exe ?

JM M


(If times count, of course. Im waiting for one cheap q-computer)
JM Montolio A is offline   Reply With Quote
Old 2018-02-27, 15:47   #18
JM Montolio A
 
Feb 2018

25·3 Posts
Default

relating m order of 2 mod p:

Any idea of what it means. :-)

JM M
JM Montolio A is offline   Reply With Quote
Old 2018-02-27, 15:55   #19
JM Montolio A
 
Feb 2018

25·3 Posts
Default

pseudocode tserie
init vars:
M=0, e=eStart, D=1, PD=1.
begin
loop
Use the step equation to get g, e'

M =M+g
PD =PD*(2^g)
Si (e')!=(eEnd), D=D+PD
e =e'

Exit loop when "e=eEnd";
loopend

return values M,D.
end


For the M() function, the step eq. is n+e = (2^g)*(e')
eStart=1
eEnd=1
JM Montolio A is offline   Reply With Quote
Old 2018-02-27, 16:20   #20
JM Montolio A
 
Feb 2018

25·3 Posts
Default

Someone asked to "a1call" values of 64 bits for their rev-fact.
Well here someones of 30b, now.

M M 52667 n 1073814919 Nbit 10 D 0 Dbit 26123 Mi 52667

M M 5711 n 1073814943 Nbit 12 D 0 Dbit 2851 Mi 5711

M M 18979 n 1073815079 Nbit 10 D 0 Dbit 9526 Mi 18979

w M 22 n 1073815151 Nbit 12 D 2097009 Dbit 17 Mi 11


M M 14639 n 1073815187 Nbit 10 D 0 Dbit 7234 Mi 14639

w M 13474 n 1073815447 Nbit 12 D 0 Dbit 6700 Mi 6737

w M 2066 n 1073815507 Nbit 12 D 0 Dbit 1021 Mi 1033

w M 18982 n 1073815531 Nbit 13 D 0 Dbit 9476 Mi 9491

M M 52553 n 1073815759 Nbit 9 D 0 Dbit 26315 Mi 52553

w M 13274 n 1073815933 Nbit 10 D 0 Dbit 6747 Mi 6637

Explain:

n, M(n).

n*D = 2^M-1

Si D is unknow, we know the number of bits ONE of D.

Mi : part odd of M. That is for Wagstaff numbers.
JM Montolio A is offline   Reply With Quote
Old 2018-03-01, 11:03   #21
JM Montolio A
 
Feb 2018

25×3 Posts
Smile A windows exe to find values of M() function.

Hi,
One free tool.
JM M

Last fiddled with by Batalov on 2018-03-01 at 15:45 Reason: blind executable attachment is removed
JM Montolio A is offline   Reply With Quote
Old 2018-03-01, 15:44   #22
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

23·7·163 Posts
Default

You can only attach the executables after you have demonstrated the source.
We don't need potential malware on this site.
Attachment deleted.
Batalov is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Fun with partition function Batalov And now for something completely different 24 2018-02-27 17:03
phi function rula Homework Help 3 2017-01-18 01:41
Gamma function Calvin Culus Analysis & Analytic Number Theory 6 2010-12-23 22:18
Solve for mod function flouran Miscellaneous Math 23 2009-01-04 20:03
Quick mod function ? dsouza123 Math 16 2004-03-04 13:57

All times are UTC. The time now is 22:02.

Tue Oct 27 22:02:21 UTC 2020 up 47 days, 19:13, 2 users, load averages: 1.96, 2.07, 2.03

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

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.